Condensed matter physics: Difference between revisions

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Template:Short description Template:Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.^[1]

The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists,^[2] and the Division of Condensed Matter Physics is the largest division of the American Physical Society.^[3] These include solid state and soft matter physicists, who study quantum and non-quantum physical properties of matter respectively.^[4] Both types study a great range of materials, providing many research, funding and employment opportunities.^[5] The field overlaps with chemistry, materials science, engineering and nanotechnology, and relates closely to atomic physics and biophysics. The theoretical physics of condensed matter shares important concepts and methods with that of particle physics and nuclear physics.^[6]

A variety of topics in physics such as crystallography, metallurgy, elasticity, magnetism, etc., were treated as distinct areas until the 1940s, when they were grouped together as solid-state physics. Around the 1960s, the study of physical properties of liquids was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics.^[7] The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics.^[7] According to the founding director of the Max Planck Institute for Solid State Research, physics professor Manuel Cardona, it was Albert Einstein who created the modern field of condensed matter physics starting with his seminal 1905 article on the photoelectric effect and photoluminescence which opened the fields of photoelectron spectroscopy and photoluminescence spectroscopy, and later his 1907 article on the specific heat of solids which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the specific heat.^[8] Deputy Director of the Yale Quantum Institute A. Douglas Stone makes a similar priority case for Einstein in his work on the synthetic history of quantum mechanics.^[9]

Etymology

According to physicist Philip Warren Anderson, the use of the term "condensed matter" to designate a field of study was coined by him and Volker Heine, when they changed the name of their group at the Cavendish Laboratories, Cambridge, from Solid state theory to Theory of Condensed Matter in 1967,^[10] as they felt it better included their interest in liquids, nuclear matter, and so on.^[11]^[12] Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the Springer-Verlag journal Physics of Condensed Matter, launched in 1963.^[13] The name "condensed matter physics" emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, whereas "solid state physics" was often associated with restricted industrial applications of metals and semiconductors. In the 1960s and 70s, some physicists felt the more comprehensive name better fit the funding environment and Cold War politics of the time.^[14]

References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids,^[15] Yakov Frenkel proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies. As a matter of fact, it would be more correct to unify them under the title of 'condensed bodiesTemplate:'".

History

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Classical physics

File:Heike Kamerlingh Onnes and Johannes Diderik van der Waals.jpg

Heike Kamerlingh Onnes and Johannes van der Waals with the helium liquefactor at Leiden in 1908

One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity.^[16] This indicated that the atoms in John Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as nitrogen and hydrogen could be liquefied under the right conditions and would then behave as metals.^[17]Template:NoteTag

In 1823, Michael Faraday, then an assistant in Davy's lab, successfully liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and oxygen.^[16] Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases,^[18] and Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.^[19]Template:Rp By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and the then newly discovered helium respectively.^[16]

Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid.^[6] Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the Wiedemann–Franz law.^[20]^[21]Template:Rp However, despite the success of Drude's model, it had one notable problem: it was unable to correctly explain the electronic contribution to the specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.^[22]Template:Rp

In 1911, three years after helium was first liquefied, Onnes working at University of Leiden discovered superconductivity in mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.^[23] The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.^[24] Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."^[25]

Advent of quantum mechanics

Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the Fermi–Dirac statistics. Using this idea, he developed the theory of paramagnetism in 1926. Shortly after, Sommerfeld incorporated the Fermi–Dirac statistics into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used quantum mechanics to describe the motion of an electron in a periodic lattice.^[22]Template:Rp

The mathematics of crystal structures developed by Auguste Bravais, Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935.^[26] Band structure calculations were first used in 1930 to predict the properties of new materials, and in 1947 John Bardeen, Walter Brattain and William Shockley developed the first semiconductor-based transistor, heralding a revolution in electronics.^[6]

File:Replica-of-first-transistor.jpg

A replica of the first point-contact transistor in Bell labs

In 1879, Edwin Herbert Hall working at the Johns Hopkins University discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.^[27] This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the Hall effect, but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, Lev Landau in 1930 developed the theory of Landau quantization and laid the foundation for a theoretical explanation of the quantum Hall effect which was discovered half a century later.^[28]Template:Rp^[29]

Magnetism as a property of matter has been known in China since 4000 BC.^[30]Template:Rp However, the first modern studies of magnetism only started with the development of electrodynamics by Faraday, Maxwell and others in the nineteenth century, which included classifying materials as ferromagnetic, paramagnetic and diamagnetic based on their response to magnetization.^[31] Pierre Curie studied the dependence of magnetization on temperature and discovered the Curie point phase transition in ferromagnetic materials.^[30] In 1906, Pierre Weiss introduced the concept of magnetic domains to explain the main properties of ferromagnets.^[32]Template:Rp The first attempt at a microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic lattice of spins that collectively acquired magnetization.^[30] The Ising model was solved exactly to show that spontaneous magnetization can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on spin waves and Néel on antiferromagnetism led to developing new magnetic materials with applications to magnetic storage devices.^[30]Template:Rp

Modern many-body physics

A magnet levitating over a superconducting material.

A magnet levitating above a high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.^[33]

The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of superconductivity and the Kondo effect.^[34] After World War II, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of collective excitation modes of solids and the important notion of a quasiparticle. Soviet physicist Lev Landau used the idea for the Fermi liquid theory wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.^[34] Landau also developed a mean-field theory for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry. The theory also introduced the notion of an order parameter to distinguish between ordered phases.^[35] Eventually in 1956, John Bardeen, Leon Cooper and Robert Schrieffer developed the so-called BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by phonons in the lattice can give rise to a bound state called a Cooper pair.^[36]

File:Quantum Hall effect - Russian.png

The quantum Hall effect: Components of the Hall resistivity as a function of the external magnetic field^[37]Template:Rp

The study of phase transitions and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s.^[38] Leo Kadanoff, Benjamin Widom and Michael Fisher developed the ideas of critical exponents and widom scaling. These ideas were unified by Kenneth G. Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.^[38]

The quantum Hall effect was discovered by Klaus von Klitzing, Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant $e^{2} / h$ .(see figure) The effect was observed to be independent of parameters such as system size and impurities.^[37] In 1981, theorist Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, called Chern number, whose relevance for the band structure of solids was formulated by David J. Thouless and collaborators.^[39]^[40]Template:Rp Shortly after, in 1982, Horst Störmer and Daniel Tsui observed the fractional quantum Hall effect where the conductance was now a rational multiple of the constant $e^{2} / h$ . Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational method solution, named the Laughlin wavefunction.^[41] The study of topological properties of the fractional Hall effect remains an active field of research.^[42] Decades later, the aforementioned topological band theory advanced by David J. Thouless and collaborators^[43] was further expanded leading to the discovery of topological insulators.^[44]^[45]

In 1986, Karl Müller and Johannes Bednorz discovered the first high temperature superconductor, La_2-xBa_xCuO₄, which is superconducting at temperatures as high as 39 kelvin.^[46] It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.^[47] A satisfactory theoretical description of high-temperature superconductors is still not known and the field of strongly correlated materials continues to be an active research topic.

In 2012, several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator^[48] in accord with the earlier theoretical predictions.^[49] Since samarium hexaboride is an established Kondo insulator, i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.

Theoretical

Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as the Drude model, the band structure and the density functional theory. Theoretical models have also been developed to study the physics of phase transitions, such as the Ginzburg–Landau theory, critical exponents and the use of mathematical methods of quantum field theory and the renormalization group. Modern theoretical studies involve the use of numerical computation of electronic structure and mathematical tools to understand phenomena such as high-temperature superconductivity, topological phases, and gauge symmetries.

Emergence

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Theoretical understanding of condensed matter physics is closely related to the notion of emergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents.^[36]^[42] For example, a range of phenomena related to high temperature superconductivity are understood poorly, although the microscopic physics of individual electrons and lattices is well known.^[50] Similarly, models of condensed matter systems have been studied where collective excitations behave like photons and electrons, thereby describing electromagnetism as an emergent phenomenon.^[51] Emergent properties can also occur at the interface between materials: one example is the lanthanum aluminate-strontium titanate interface, where two band-insulators are joined to create conductivity and superconductivity.

Electronic theory of solids

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The metallic state has historically been an important building block for studying properties of solids.^[52] The first theoretical description of metals was given by Paul Drude in 1900 with the Drude model, which explained electrical and thermal properties by describing a metal as an ideal gas of then-newly discovered electrons. He was able to derive the empirical Wiedemann-Franz law and get results in close agreement with the experiments.^[21]Template:Rp This classical model was then improved by Arnold Sommerfeld who incorporated the Fermi–Dirac statistics of electrons and was able to explain the anomalous behavior of the specific heat of metals in the Wiedemann–Franz law.^[21]Template:Rp In 1912, The structure of crystalline solids was studied by Max von Laue and Paul Knipping, when they observed the X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms.^[21]Template:Rp^[53] In 1928, Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, known as Bloch's theorem.^[54]

Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions.^[55] The Thomas–Fermi theory, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a variational parameter. Later in the 1930s, Douglas Hartree, Vladimir Fock and John Slater developed the so-called Hartree–Fock wavefunction as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for exchange statistics of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly.^[52]Template:Rp Finally in 1964–65, Walter Kohn, Pierre Hohenberg and Lu Jeu Sham proposed the density functional theory (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.^[55]

Symmetry breaking

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Some states of matter exhibit symmetry breaking, where the relevant laws of physics possess some form of symmetry that is broken. A common example is crystalline solids, which break continuous translational symmetry. Other examples include magnetized ferromagnets, which break rotational symmetry, and more exotic states such as the ground state of a BCS superconductor, that breaks U(1) phase rotational symmetry.^[56]^[57]

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons. For example, in crystalline solids, these correspond to phonons, which are quantized versions of lattice vibrations.^[58]

Phase transition

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Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as temperature, pressure, or molar composition. In a single-component system, a classical phase transition occurs at a temperature (at a specific pressure) where there is an abrupt change in the order of the system. For example, when ice melts and becomes water, the ordered hexagonal crystal structure of ice is modified to a hydrogen bonded, mobile arrangement of water molecules.

In quantum phase transitions, the temperature is set to absolute zero, and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed by quantum fluctuations originating from the Heisenberg uncertainty principle. Here, the different quantum phases of the system refer to distinct ground states of the Hamiltonian matrix. Understanding the behavior of quantum phase transition is important in the difficult tasks of explaining the properties of rare-earth magnetic insulators, high-temperature superconductors, and other substances.^[59]

Two classes of phase transitions occur: first-order transitions and second-order or continuous transitions. For the latter, the two phases involved do not co-exist at the transition temperature, also called the critical point. Near the critical point, systems undergo critical behavior, wherein several of their properties such as correlation length, specific heat, and magnetic susceptibility diverge exponentially.^[59] These critical phenomena present serious challenges to physicists because normal macroscopic laws are no longer valid in the region, and novel ideas and methods must be invented to find the new laws that can describe the system.^[60]Template:Rp

The simplest theory that can describe continuous phase transitions is the Ginzburg–Landau theory, which works in the so-called mean-field approximation. However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions. For other types of systems that involves short range interactions near the critical point, a better theory is needed.^[61]Template:Rp

Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant. Renormalization group methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage. Thus, the changes of a physical system as viewed at different size scales can be investigated systematically. The methods, together with powerful computer simulation, contribute greatly to the explanation of the critical phenomena associated with continuous phase transition.^[60]Template:Rp

Experimental

Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of electric and magnetic fields, measuring response functions, transport properties and thermometry.^[62] Commonly used experimental methods include spectroscopy, with probes such as X-rays, infrared light and inelastic neutron scattering; study of thermal response, such as specific heat and measuring transport via thermal and heat conduction.

File:Lysozym diffraction.png

Image of X-ray diffraction pattern from a protein crystal

Scattering

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Several condensed matter experiments involve scattering of an experimental probe, such as X-ray, optical photons, neutrons, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest. Visible light has energy on the scale of 1 electron volt (eV) and is used as a scattering probe to measure variations in material properties such as the dielectric constant and refractive index. X-rays have energies of the order of 10 keV and hence are able to probe atomic length scales, and are used to measure variations in electron charge density and crystal structure.^[63]Template:Rp

Neutrons can also probe atomic length scales and are used to study the scattering off nuclei and electron spins and magnetization (as neutrons have spin but no charge). Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes.^[63]Template:Rp^[64]Template:Rp Similarly, positron annihilation can be used as an indirect measurement of local electron density.^[65] Laser spectroscopy is an excellent tool for studying the microscopic properties of a medium, for example, to study forbidden transitions in media with nonlinear optical spectroscopy.^[60] Template:Rp

External magnetic fields

In experimental condensed matter physics, external magnetic fields act as thermodynamic variables that control the state, phase transitions and properties of material systems.^[66] Nuclear magnetic resonance (NMR) is a method by which external magnetic fields are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60 tesla. Higher magnetic fields can improve the quality of NMR measurement data.^[67]Template:Rp^[68]Template:Rp Quantum oscillations is another experimental method where high magnetic fields are used to study material properties such as the geometry of the Fermi surface.^[69] High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized magnetoelectric effect, image magnetic monopole, and the half-integer quantum Hall effect.^[67]Template:Rp

Magnetic resonance spectroscopy

The local structure, as well as the structure of the nearest neighbour atoms, can be investigated in condensed matter with magnetic resonance methods, such as electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR), which are very sensitive to the details of the surrounding of nuclei and electrons by means of the hyperfine coupling. Both localized electrons and specific stable or unstable isotopes of the nuclei become the probe of these hyperfine interactions), which couple the electron or nuclear spin to the local electric and magnetic fields. These methods are suitable to study defects, diffusion, phase transitions and magnetic order. Common experimental methods include NMR, nuclear quadrupole resonance (NQR), implanted radioactive probes as in the case of muon spin spectroscopy ( $μ$ SR), Mössbauer spectroscopy, $β$ NMR and perturbed angular correlation (PAC). PAC is especially ideal for the study of phase changes at extreme temperatures above 2000 °C due to the temperature independence of the method.

Cold atomic gases

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File:Bose Einstein condensate.png

The first Bose–Einstein condensate observed in a gas of ultracold rubidium atoms. The blue and white areas represent higher density.

Ultracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in atomic, molecular, and optical physics. The method involves using optical lasers to form an interference pattern, which acts as a lattice, in which ions or atoms can be placed at very low temperatures. Cold atoms in optical lattices are used as quantum simulators, that is, they act as controllable systems that can model behavior of more complicated systems, such as frustrated magnets.^[70] In particular, they are used to engineer one-, two- and three-dimensional lattices for a Hubbard model with pre-specified parameters, and to study phase transitions for antiferromagnetic and spin liquid ordering.^[71]^[72]^[42]

In 1995, a gas of rubidium atoms cooled down to a temperature of 170 nK was used to experimentally realize the Bose–Einstein condensate, a novel state of matter originally predicted by S. N. Bose and Albert Einstein, wherein a large number of atoms occupy one quantum state.^[73]

Applications

File:Fullerene Nanogears - GPN-2000-001535.jpg

Computer simulation of nanogears made of fullerene molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.

Research in condensed matter physics^[42]^[74] has given rise to several device applications, such as the development of the semiconductor transistor,^[6] laser technology,^[60] magnetic storage, liquid crystals, optical fibres^[75] and several phenomena studied in the context of nanotechnology.^[76]Template:Rp Methods such as scanning-tunneling microscopy can be used to control processes at the nanometer scale, and have given rise to the study of nanofabrication.^[77] Such molecular machines were developed for example by Nobel laureates in chemistry Ben Feringa, Jean-Pierre Sauvage and Fraser Stoddart. Feringa and his team developed multiple molecular machines such as the molecular car, molecular windmill and many more.^[78]

In quantum computation, information is represented by quantum bits, or qubits. The qubits may decohere quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, including Josephson junction qubits, spintronic qubits using the spin orientation of magnetic materials, and the topological non-Abelian anyons from fractional quantum Hall effect states.^[77]

Condensed matter physics also has important uses for biomedicine. For example, magnetic resonance imaging is widely used in medical imaging of soft tissue and other physiological features which cannot be viewed with traditional x-ray imaging.^[77]

Notes

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References

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External links

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 '''Condensed matter physics''' is the field of [[physics]] that deals with the macroscopic and microscopic physical properties of [[matter]], especially the [[solid]] and [[liquid]] [[State of matter|phases]], that arise from [[electromagnetic]] forces between [[atom]]s and [[electrons]].  More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the [[superconductivity|superconducting]] phase exhibited by certain materials at extremely low [[cryogenic]] [[temperature]]s, the [[ferromagnet]]ic and [[antiferromagnet]]ic phases of [[Spin (physics)|spins]] on [[crystal lattice]]s of atoms, the [[Bose–Einstein condensates]] found in [[ultracold atom]]ic systems, and [[liquid crystals]]. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the [[physical law]]s of [[quantum mechanics]], [[electromagnetism]], [[statistical mechanics]], and other [[theoretical physics|physics theories]] to develop mathematical models and predict the properties of extremely large groups of atoms.<ref>{{cite web|url=https://physics.yale.edu/research/condensed-matter-physics-theory|title=Condensed Matter Physics Theory|website=Yale University Physics Department|access-date= 2023-11-30}}</ref>
-The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists,<ref>{{cite web|url= http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-url= https://web.archive.org/web/20090327141400/http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-date= 2009-03-27|website=Physics Today Jobs|title= Condensed Matter Physics Jobs: Careers in Condensed Matter Physics|access-date= 2010-11-01}}</ref> and the Division of Condensed Matter Physics is the largest division of the [[American Physical Society]].<ref name=aps-history>{{cite web|title=History of Condensed Matter Physics|url=http://www.aps.org/units/dcmp/history.cfm|publisher=American Physical Society|access-date=27 March 2012}}</ref> These include solid state and [[soft matter]] physicists, who study [[quantum mechanics|quantum]] and non-quantum physical properties of matter respectively.<ref>{{cite web|title=Condensed Matter Physics|url=https://www.colorado.edu/physics/research/condensed-matter-physics |website=University of Colorado Boulder Physics Department|date=26 April 2016 |access-date=2023-11-30}}</ref> Both types study a great range of materials, providing many research, funding and employment opportunities.<ref>{{cite web|title=Condensed Matter and Materials Physics|url=https://physics.uiowa.edu/research/condensed-matter-and-materials-physics|website=Iowa College of Liberal Arts and Sciences|access-date=2023-11-30}}</ref> The field overlaps with [[chemistry]], [[materials science]], [[engineering]] and [[nanotechnology]], and relates closely to [[atomic physics]] and [[biophysics]]. The [[theoretical physics]] of condensed matter shares important concepts and methods with that of [[particle physics]] and [[nuclear physics]].<ref name=marvincohen2008>{{cite journal|last=Cohen|first=Marvin L.|title=Essay: Fifty Years of Condensed Matter Physics|journal=Physical Review Letters|year=2008|volume=101|issue=25|doi=10.1103/PhysRevLett.101.250001|url=http://prl.aps.org/edannounce/PhysRevLett.101.250001|access-date=31 March 2012|bibcode= 2008PhRvL.101y0001C|pmid=19113681|page=250001}}</ref>
+The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists,<ref>{{cite web|url= http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-url= https://web.archive.org/web/20090327141400/http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-date= 2009-03-27|website=Physics Today Jobs|title= Condensed Matter Physics Jobs: Careers in Condensed Matter Physics|access-date= 2010-11-01}}</ref> and the Division of Condensed Matter Physics is the largest division of the [[American Physical Society]].<ref name=aps-history>{{cite web|title=History of Condensed Matter Physics|url=http://www.aps.org/units/dcmp/history.cfm|publisher=American Physical Society|access-date=27 March 2012}}</ref> These include solid state and [[soft matter]] physicists, who study [[quantum mechanics|quantum]] and non-quantum physical properties of matter respectively.<ref>{{cite web|title=Condensed Matter Physics|url=https://www.colorado.edu/physics/research/condensed-matter-physics |website=University of Colorado Boulder Physics Department|date=26 April 2016 |access-date=2023-11-30}}</ref> Both types study a great range of materials, providing many research, funding and employment opportunities.<ref>{{cite web|title=Condensed Matter and Materials Physics|url=https://physics.uiowa.edu/research/condensed-matter-and-materials-physics|website=Iowa College of Liberal Arts and Sciences|access-date=2023-11-30}}</ref> The field overlaps with [[chemistry]], [[materials science]], [[engineering]] and [[nanotechnology]], and relates closely to [[atomic physics]] and [[biophysics]]. The [[theoretical physics]] of condensed matter shares important concepts and methods with that of [[particle physics]] and [[nuclear physics]].<ref name=marvincohen2008>{{cite journal|last=Cohen|first=Marvin L.|title=Essay: Fifty Years of Condensed Matter Physics|journal=Physical Review Letters|year=2008|volume=101|issue=25|doi=10.1103/PhysRevLett.101.250001|url=http://prl.aps.org/edannounce/PhysRevLett.101.250001|access-date=31 March 2012|bibcode= 2008PhRvL.101y0001C|pmid=19113681|article-number=250001}}</ref>
-A variety of topics in physics such as [[crystallography]], [[metallurgy]], [[elasticity (physics)|elasticity]], [[magnetism]], etc., were treated as distinct areas until the 1940s, when they were grouped together as ''[[solid-state physics]]''. Around the 1960s, the study of physical properties of [[liquid]]s was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics.<ref name=rmp /> The [[Bell Labs|Bell Telephone Laboratories]] was one of the first institutes to conduct a research program in condensed matter physics.<ref name=rmp>{{cite journal|last=Kohn|first=W.|title=An essay on condensed matter physics in the twentieth century|journal=Reviews of Modern Physics|year=1999|volume=71|issue=2|url= http://nanoelectronics.unibas.ch/education/ModernPhysics/KohnCondMat.pdf |access-date=27 March 2012|doi=10.1103/RevModPhys.71.S59|pages= S59–S77 |bibcode= 1999RvMPS..71...59K|url-status=dead|archive-url=https://web.archive.org/web/20130825164926/http://nanoelectronics.unibas.ch/education/ModernPhysics/KohnCondMat.pdf|archive-date=25 August 2013}}</ref> According to the founding director of the [[Max Planck Institute for Solid State Research]], physics professor Manuel Cardona, it was [[Albert Einstein]] who created the modern field of condensed matter physics starting with his seminal 1905 article on the [[photoelectric effect]] and [[photoluminescence]] which opened the fields of [[photoelectron spectroscopy]] and [[photoluminescence spectroscopy]], and later his 1907 article on the [[specific heat of solids]] which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the [[specific heat]].<ref name="Cardona">{{cite arXiv |last1=Cardona |first1=Manuel |title=Einstein as the Father of Solid State Physics |eprint=physics/0508237|date=31 August 2005}}</ref> Deputy Director of the Yale Quantum Institute [[A. Douglas Stone]] makes a similar priority case for Einstein in his work on the synthetic history of [[quantum mechanics]].<ref name="Stone">{{cite book |last1=Stone |first1=A. Douglas |title=Einstein and the Quantum: The Quest of the Valiant Swabian |date=6 October 2013 |publisher=Princeton University Press |isbn=978-0691139685 |edition=First |url=https://press.princeton.edu/books/paperback/9780691168562/einstein-and-the-quantum |access-date=1 June 2022}}</ref>
+A variety of topics in physics such as [[crystallography]], [[metallurgy]], [[elasticity (physics)|elasticity]], [[magnetism]], etc., were treated as distinct areas until the 1940s, when they were grouped together as ''[[solid-state physics]]''. Around the 1960s, the study of physical properties of [[liquid]]s was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics.<ref name=rmp /> The [[Bell Labs|Bell Telephone Laboratories]] was one of the first institutes to conduct a research program in condensed matter physics.<ref name=rmp>{{cite journal|last=Kohn|first=W.|title=An essay on condensed matter physics in the twentieth century|journal=Reviews of Modern Physics|year=1999|volume=71|issue=2|url= http://nanoelectronics.unibas.ch/education/ModernPhysics/KohnCondMat.pdf |access-date=27 March 2012|doi=10.1103/RevModPhys.71.S59|pages= S59–S77 |bibcode= 1999RvMPS..71...59K|archive-url=https://web.archive.org/web/20130825164926/http://nanoelectronics.unibas.ch/education/ModernPhysics/KohnCondMat.pdf|archive-date=25 August 2013}}</ref> According to the founding director of the [[Max Planck Institute for Solid State Research]], physics professor Manuel Cardona, it was [[Albert Einstein]] who created the modern field of condensed matter physics starting with his seminal 1905 article on the [[photoelectric effect]] and [[photoluminescence]] which opened the fields of [[photoelectron spectroscopy]] and [[photoluminescence spectroscopy]], and later his 1907 article on the [[specific heat of solids]] which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the [[specific heat]].<ref name="Cardona">{{cite arXiv |last1=Cardona |first1=Manuel |title=Einstein as the Father of Solid State Physics |eprint=physics/0508237|date=31 August 2005}}</ref> Deputy Director of the Yale Quantum Institute [[A. Douglas Stone]] makes a similar priority case for Einstein in his work on the synthetic history of [[quantum mechanics]].<ref name="Stone">{{cite book |last1=Stone |first1=A. Douglas |title=Einstein and the Quantum: The Quest of the Valiant Swabian |date=6 October 2013 |publisher=Princeton University Press |isbn=978-0-691-13968-5 |edition=First |url=https://press.princeton.edu/books/paperback/9780691168562/einstein-and-the-quantum |access-date=1 June 2022}}</ref>
 ==Etymology==
@@ Line 19: / Line 19: @@
 [[File:Heike Kamerlingh Onnes and Johannes Diderik van der Waals.jpg|thumb|upright|[[Heike Kamerlingh Onnes]] and [[Johannes van der Waals]] with the [[helium]] ''liquefactor'' at Leiden in 1908]]
-One of the first studies of condensed states of matter was by [[People of England|English]] [[chemist]] [[Humphry Davy]], in the first decades of the nineteenth century. Davy observed that of the forty [[chemical element]]s known at the time, twenty-six had [[metal]]lic properties such as [[lustre (mineralogy)|lustre]], [[ductility]] and high electrical and thermal conductivity.<ref name=goodstein>{{cite journal|last1=Goodstein|first1=David|author1-link=David Goodstein|last2=Goodstein|first2=Judith|author2-link=Judith R. Goodstein|title=Richard Feynman and the History of Superconductivity|journal=Physics in Perspective|year=2000|volume=2|issue=1|url=http://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|access-date=7 April 2012|doi=10.1007/s000160050035|pages=30|bibcode=2000PhP.....2...30G|s2cid=118288008|archive-url=https://web.archive.org/web/20151117113759/https://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|archive-date=17 November 2015|url-status=dead}}</ref> This indicated that the atoms in [[John Dalton]]'s [[atomic theory]] were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as [[nitrogen]] and [[hydrogen]] could be liquefied under the right conditions and would then behave as metals.<ref name=davy-1839>{{cite book |editor-last=Davy |editor-first = John |title=The collected works of Sir Humphry Davy: Vol. II |year=1839|publisher=Smith Elder & Co., Cornhill |url = https://archive.org/details/bub_gb_6WNKAAAAYAAJ |page=[https://archive.org/details/bub_gb_6WNKAAAAYAAJ/page/n34 22] }}</ref>{{NoteTag|Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists [[Eugene Wigner]] and [[Hillard Bell Huntington]] predicted in 1935<ref name=metallic-hydrogen>{{cite journal |last=Silvera|first=Isaac F.|author2=Cole, John W. |title=Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist|journal=Journal of Physics|year=2010|volume=215|issue=1 |doi=10.1088/1742-6596/215/1/012194 |bibcode= 2010JPhCS.215a2194S |pages=012194 |url = http://nrs.harvard.edu/urn-3:HUL.InstRepos:9569212 |doi-access=free}}</ref> that a state [[metallic hydrogen]] exists at sufficiently high pressures (over 25 [[Pascal (unit)|GPa]]), but this has not yet been observed.}}
+One of the first studies of condensed states of matter was by [[People of England|English]] [[chemist]] [[Humphry Davy]], in the first decades of the nineteenth century. Davy observed that of the forty [[chemical element]]s known at the time, twenty-six had [[metal]]lic properties such as [[lustre (mineralogy)|lustre]], [[ductility]] and high electrical and thermal conductivity.<ref name=goodstein>{{cite journal|last1=Goodstein|first1=David|author1-link=David Goodstein|last2=Goodstein|first2=Judith|author2-link=Judith R. Goodstein|title=Richard Feynman and the History of Superconductivity|journal=Physics in Perspective|year=2000|volume=2|issue=1|url=http://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|access-date=7 April 2012|doi=10.1007/s000160050035|page=30|bibcode=2000PhP.....2...30G|s2cid=118288008|archive-url=https://web.archive.org/web/20151117113759/https://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|archive-date=17 November 2015}}</ref> This indicated that the atoms in [[John Dalton]]'s [[atomic theory]] were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as [[nitrogen]] and [[hydrogen]] could be liquefied under the right conditions and would then behave as metals.<ref name=davy-1839>{{cite book |editor-last=Davy |editor-first = John |title=The collected works of Sir Humphry Davy: Vol. II |year=1839|publisher=Smith Elder & Co., Cornhill |url = https://archive.org/details/bub_gb_6WNKAAAAYAAJ |page=[https://archive.org/details/bub_gb_6WNKAAAAYAAJ/page/n34 22] }}</ref>{{NoteTag|Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists [[Eugene Wigner]] and [[Hillard Bell Huntington]] predicted in 1935<ref name=metallic-hydrogen>{{cite journal |last=Silvera|first=Isaac F.|author2=Cole, John W. |title=Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist|journal=Journal of Physics|year=2010|volume=215|issue=1 |doi=10.1088/1742-6596/215/1/012194 |bibcode= 2010JPhCS.215a2194S |article-number=012194 |url = http://nrs.harvard.edu/urn-3:HUL.InstRepos:9569212 |doi-access=free}}</ref> that a state [[metallic hydrogen]] exists at sufficiently high pressures (over 25 [[Pascal (unit)|GPa]]), but this has not yet been observed.}}
 In 1823, [[Michael Faraday]], then an assistant in Davy's lab, successfully liquefied [[chlorine]] and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and [[oxygen]].<ref name=goodstein /> Shortly after, in 1869, [[People of Ireland|Irish]] chemist [[Thomas Andrews (scientist)|Thomas Andrews]] studied the [[phase transition]] from a liquid to a gas and coined the term [[Critical point (thermodynamics)|critical point]] to describe the condition where a gas and a liquid were indistinguishable as phases,<ref name=thomasandrews>{{cite journal|last=Rowlinson|first=J. S.|title=Thomas Andrews and the Critical Point|journal=Nature|year=1969|volume=224|issue=8|doi=10.1038/224541a0|pages=541–543|bibcode= 1969Natur.224..541R|s2cid=4168392}}</ref> and [[Netherlands|Dutch]] physicist [[Johannes van der Waals]] supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.<ref name=atkins>{{cite book|last1=Atkins|first1=Peter|last2=de Paula|first2=Julio|title=Elements of Physical Chemistry|year=2009|publisher=Oxford University Press|isbn=978-1-4292-1813-9}}</ref>{{rp|35–38}} By 1908, [[James Dewar]] and [[Heike Kamerlingh Onnes]] were successfully able to liquefy hydrogen and the then newly discovered [[helium]] respectively.<ref name=goodstein />
@@ Line 25: / Line 25: @@
 [[Paul Drude]] in 1900 proposed the first theoretical model for a classical [[electron]] moving through a metallic solid.<ref name=marvincohen2008 /> Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the [[Wiedemann–Franz law]].<ref name="Kittel 1996">{{cite book|last=Kittel|first=Charles|title=[[Introduction to Solid State Physics]]|year=1996|publisher=John Wiley & Sons|isbn=978-0-471-11181-8}}</ref><ref name=Hoddeson-1992>{{cite book|last=Hoddeson|first=Lillian|title=Out of the Crystal Maze: Chapters from The History of Solid State Physics|year=1992|publisher=Oxford University Press|isbn=978-0-19-505329-6|url=https://books.google.com/books?id=WCpPPHhMdRcC&pg=PA29}}</ref>{{rp|27–29}} However, despite the success of [[Drude model|Drude's model]], it had one notable problem: it was unable to correctly explain the electronic contribution to the [[specific heat]] and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.<ref name=Kragh2002>{{cite book |last= Kragh |first= Helge |title= Quantum Generations: A History of Physics in the Twentieth Century |publisher= Princeton University Press |edition= Reprint |date= 2002 |isbn= 978-0-691-09552-3}}</ref>{{rp|366–368}}
-In 1911, three years after helium was first liquefied, Onnes working at [[University of Leiden]] discovered [[superconductivity]] in [[mercury (element)|mercury]], when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.<ref name=vanDelft2010>{{cite journal|last=van Delft|first=Dirk|author2=Kes, Peter |title=The discovery of superconductivity|journal=Physics Today|date=September 2010|volume=63|issue=9|doi=10.1063/1.3490499|url=http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-date=2022-10-09 |url-status=live|access-date=7 April 2012|bibcode= 2010PhT....63i..38V|pages=38–43|doi-access=free}}</ref> The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.<ref name=Slichter-AIP-supercond>{{cite web|last=Slichter|first=Charles|title=Introduction to the History of Superconductivity|url=http://www.aip.org/history/mod/superconductivity/01.html|website=Moments of Discovery|publisher=American Institute of Physics|access-date=13 June 2012|archive-url=https://web.archive.org/web/20120515123519/http://www.aip.org/history/mod/superconductivity/01.html|archive-date=15 May 2012|url-status=dead}}</ref> [[Albert Einstein]], in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."<ref name=Schmalian-2010>{{cite journal|last=Schmalian|first=Joerg|title=Failed theories of superconductivity|year=2010|arxiv=1008.0447|bibcode= 2010MPLB...24.2679S |doi= 10.1142/S0217984910025280|journal=Modern Physics Letters B|volume=24|issue=27|pages=2679–2691|s2cid=119220454}}</ref>
+In 1911, three years after helium was first liquefied, Onnes working at [[University of Leiden]] discovered [[superconductivity]] in [[mercury (element)|mercury]], when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.<ref name=vanDelft2010>{{cite journal|last=van Delft|first=Dirk|author2=Kes, Peter |title=The discovery of superconductivity|journal=Physics Today|date=September 2010|volume=63|issue=9|doi=10.1063/1.3490499|url=http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-date=2022-10-09 |url-status=live|access-date=7 April 2012|bibcode= 2010PhT....63i..38V|pages=38–43|doi-access=free}}</ref> The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.<ref name=Slichter-AIP-supercond>{{cite web|last=Slichter|first=Charles|title=Introduction to the History of Superconductivity|url=http://www.aip.org/history/mod/superconductivity/01.html|website=Moments of Discovery|publisher=American Institute of Physics|access-date=13 June 2012|archive-url=https://web.archive.org/web/20120515123519/http://www.aip.org/history/mod/superconductivity/01.html|archive-date=15 May 2012}}</ref> [[Albert Einstein]], in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."<ref name=Schmalian-2010>{{cite journal|last=Schmalian|first=Joerg|title=Failed theories of superconductivity|year=2010|arxiv=1008.0447|bibcode= 2010MPLB...24.2679S |doi= 10.1142/S0217984910025280|journal=Modern Physics Letters B|volume=24|issue=27|pages=2679–2691|s2cid=119220454}}</ref>
 ===Advent of quantum mechanics===
 Drude's classical model was augmented by [[Wolfgang Pauli]], [[Arnold Sommerfeld]], [[Felix Bloch]] and other physicists.  Pauli realized that the free electrons in metal must obey the [[Fermi–Dirac statistics]].  Using this idea, he developed the theory of [[paramagnetism]] in 1926.  Shortly after, Sommerfeld incorporated the [[Fermi–Dirac statistics]] into the [[free electron model]] and made it better to explain the heat capacity.  Two years later, Bloch used [[quantum mechanics]] to describe the motion of an electron in a periodic lattice.<ref name=Kragh2002/>{{rp|366–368}}
-The mathematics of crystal structures developed by [[Auguste Bravais]], [[Yevgraf Fyodorov]] and others was used to classify crystals by their [[symmetry group]], and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935.<ref name=Aroyo-2006>{{Cite book|last=Aroyo|first=Mois, I.|author2=Müller, Ulrich|author3=Wondratschek, Hans|title=Historical introduction|year=2006|volume=A|pages=2–5|doi=10.1107/97809553602060000537|series=International Tables for Crystallography|isbn=978-1-4020-2355-2|url=http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|citeseerx=10.1.1.471.4170|access-date=2017-10-24|archive-date=2008-10-03|archive-url=https://web.archive.org/web/20081003122816/http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|url-status=dead}}</ref> [[Band theory|Band structure calculations]] were first used in 1930 to predict the properties of new materials, and in 1947 [[John Bardeen]], [[Walter Brattain]] and [[William Shockley]] developed the first [[semiconductor]]-based [[transistor]], heralding a revolution in electronics.<ref name=marvincohen2008 />
+The mathematics of crystal structures developed by [[Auguste Bravais]], [[Yevgraf Fyodorov]] and others was used to classify crystals by their [[symmetry group]], and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935.<ref name=Aroyo-2006>{{Cite book|last=Aroyo|first=Mois, I.|author2=Müller, Ulrich|author3=Wondratschek, Hans|title=Historical introduction|year=2006|volume=A|pages=2–5|doi=10.1107/97809553602060000537|series=International Tables for Crystallography|isbn=978-1-4020-2355-2|url=http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|citeseerx=10.1.1.471.4170|access-date=2017-10-24|archive-date=2008-10-03|archive-url=https://web.archive.org/web/20081003122816/http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF}}</ref> [[Band theory|Band structure calculations]] were first used in 1930 to predict the properties of new materials, and in 1947 [[John Bardeen]], [[Walter Brattain]] and [[William Shockley]] developed the first [[semiconductor]]-based [[transistor]], heralding a revolution in electronics.<ref name=marvincohen2008 />
 [[File:Replica-of-first-transistor.jpg|thumb|left|A replica of the first [[point-contact transistor]] in [[Bell labs]]]]
-In 1879, [[Edwin Herbert Hall]] working at the [[Johns Hopkins University]] discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.<ref>{{cite journal|title=On a New Action of the Magnet on Electric Currents|author=Hall, Edwin|journal=American Journal of Mathematics|volume=2|year=1879|pages=287–92|url=http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|access-date=2008-02-28|doi=10.2307/2369245|issue=3|jstor=2369245|s2cid=107500183 |url-status=dead|archive-url=https://web.archive.org/web/20070208040346/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|archive-date=2007-02-08}}</ref> This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the [[Hall effect]], but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, [[Lev Landau]] in 1930 developed the theory of [[Landau quantization]] and laid the foundation for a theoretical explanation of the [[quantum Hall effect]] which was discovered half a century later.<ref>{{cite book|first1=L. D.|last1=Landau|first2=E. M.|last2=Lifshitz|title=Quantum Mechanics: Nonrelativistic Theory|year=1977|publisher=Pergamon Press|isbn=978-0-7506-3539-4}}</ref>{{rp|458–460}}<ref>{{cite journal|title=Focus: Landmarks—Accidental Discovery Leads to Calibration Standard|date=2015-05-15|first=David|last=Lindley|journal=Physics|volume=8|page=46 |doi=10.1103/Physics.8.46}}</ref>
+In 1879, [[Edwin Herbert Hall]] working at the [[Johns Hopkins University]] discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.<ref>{{cite journal|title=On a New Action of the Magnet on Electric Currents|author=Hall, Edwin|journal=American Journal of Mathematics|volume=2|year=1879|pages=287–92|url=http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|access-date=2008-02-28|doi=10.2307/2369245|issue=3|jstor=2369245|s2cid=107500183 |archive-url=https://web.archive.org/web/20070208040346/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|archive-date=2007-02-08}}</ref> This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the [[Hall effect]], but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, [[Lev Landau]] in 1930 developed the theory of [[Landau quantization]] and laid the foundation for a theoretical explanation of the [[quantum Hall effect]] which was discovered half a century later.<ref>{{cite book|first1=L. D.|last1=Landau|first2=E. M.|last2=Lifshitz|title=Quantum Mechanics: Nonrelativistic Theory|year=1977|publisher=Pergamon Press|isbn=978-0-7506-3539-4}}</ref>{{rp|458–460}}<ref>{{cite journal|title=Focus: Landmarks—Accidental Discovery Leads to Calibration Standard|date=2015-05-15|first=David|last=Lindley|journal=Physics|volume=8|page=46 |doi=10.1103/Physics.8.46}}</ref>
-Magnetism as a property of matter has been known in China since 4000 BC.<ref name=mattis-magnetism-2006>{{cite book|last=Mattis|first=Daniel|title=The Theory of Magnetism Made Simple|year=2006|publisher=World Scientific|isbn=978-981-238-671-7}}</ref>{{rp|1–2}} However, the first modern studies of magnetism only started with the development of [[electrodynamics]] by Faraday, [[James Clerk Maxwell|Maxwell]] and others in the nineteenth century, which included classifying materials as [[ferromagnetic]], [[paramagnetic]] and [[diamagnetic]] based on their response to magnetization.<ref name=Chatterjee-2004-ferromagnetism>{{cite journal|last=Chatterjee|first=Sabyasachi|title=Heisenberg and Ferromagnetism|journal=Resonance|date=August 2004|volume=9|issue=8|doi=10.1007/BF02837578|url=http://www.ias.ac.in/describe/article/reso/009/08/0057-0066|access-date=13 June 2012|pages=57–66|s2cid=123099296}}</ref> [[Pierre Curie]] studied the dependence of magnetization on temperature and discovered the [[Curie point]] phase transition in ferromagnetic materials.<ref name=mattis-magnetism-2006 /> In 1906, [[Pierre Weiss]] introduced the concept of [[magnetic domain]]s to explain the main properties of ferromagnets.<ref name=Visintin-domains>{{cite book|last=Visintin|first=Augusto|title=Differential Models of Hysteresis|year=1994|publisher=Springer|isbn=978-3-540-54793-8|url=https://books.google.com/books?id=xZrTIDmNOlgC&pg=PA9}}</ref>{{rp|9}} The first attempt at a microscopic description of magnetism was by [[Wilhelm Lenz]] and [[Ernst Ising]] through the [[Ising model]] that described magnetic materials as consisting of a periodic lattice of [[Spin (physics)|spins]] that collectively acquired magnetization.<ref name=mattis-magnetism-2006/> The Ising model was solved exactly to show that [[spontaneous magnetization]] can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on [[spin wave]]s and [[Néel]] on [[antiferromagnetism]] led to developing new magnetic materials with applications to [[magnetic storage]] devices.<ref name=mattis-magnetism-2006/>{{rp|36–38,g48}}
+Magnetism as a property of matter has been known in China since 4000 BC.<ref name=mattis-magnetism-2006>{{cite book|last=Mattis|first=Daniel|title=The Theory of Magnetism Made Simple|year=2006|publisher=World Scientific|isbn=978-981-238-671-7}}</ref>{{rp|1–2}} However, the first modern studies of magnetism only started with the development of [[electrodynamics]] by Faraday, [[James Clerk Maxwell|Maxwell]] and others in the nineteenth century, which included classifying materials as [[ferromagnetic]], [[paramagnetic]] and [[diamagnetic]] based on their response to magnetization.<ref name=Chatterjee-2004-ferromagnetism>{{cite journal|last=Chatterjee|first=Sabyasachi|title=Heisenberg and Ferromagnetism|journal=Resonance|date=August 2004|volume=9|issue=8|doi=10.1007/BF02837578|url=http://www.ias.ac.in/describe/article/reso/009/08/0057-0066|access-date=13 June 2012|pages=57–66|s2cid=123099296}}</ref> [[Pierre Curie]] studied the dependence of magnetization on temperature and discovered the [[Curie point]] phase transition in ferromagnetic materials.<ref name=mattis-magnetism-2006 /> In 1906, [[Pierre Weiss]] introduced the concept of [[magnetic domain]]s to explain the main properties of ferromagnets.<ref name=Visintin-domains>{{cite book|last=Visintin|first=Augusto|title=Differential Models of Hysteresis|year=1994|publisher=Springer|isbn=978-3-540-54793-8|url=https://books.google.com/books?id=xZrTIDmNOlgC&pg=PA9}}</ref>{{rp|9}} The first attempt at a microscopic description of magnetism was by [[Wilhelm Lenz]] and [[Ernst Ising]] through the [[Ising model]] that described magnetic materials as consisting of a periodic lattice of [[Spin (physics)|spins]] that collectively acquired magnetization.<ref name=mattis-magnetism-2006/> The Ising model was solved exactly to show that [[spontaneous magnetization]] can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on [[spin wave]]s and [[Néel]] on [[antiferromagnetism]] led to developing new magnetic materials with applications to [[magnetic storage]] devices.<ref name=mattis-magnetism-2006/>{{rp|36–38, g48}}
 ===Modern many-body physics===
 [[File:Meissner effect p1390048.jpg|thumb|left|200px|alt=A magnet levitating over a superconducting material.|A [[magnet]] [[Meissner effect|levitating]] above a [[high-temperature superconductor]]. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.<ref>{{cite journal |last1= Merali |first1= Zeeya |title= Collaborative physics: string theory finds a bench mate |journal= Nature |volume= 478 |pages= 302–304 |year= 2011 |doi= 10.1038/478302a |pmid= 22012369 |issue= 7369|bibcode= 2011Natur.478..302M|doi-access= free }}</ref>]]
-The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of [[superconductivity]] and the [[Kondo effect]].<ref name=Coleman-2003>{{cite journal|last=Coleman|first=Piers|title=Many-Body Physics: Unfinished Revolution|journal=Annales Henri Poincaré|year=2003|volume=4|issue=2|doi=10.1007/s00023-003-0943-9|arxiv=cond-mat/0307004|bibcode= 2003AnHP....4..559C|pages=559–580|citeseerx=10.1.1.242.6214|s2cid=8171617}}</ref> After [[World War II]], several ideas from quantum field theory were applied to condensed matter problems. These included recognition of [[collective excitation]] modes of solids and the important notion of a quasiparticle. Soviet physicist [[Lev Landau]] used the idea for the [[Fermi liquid theory]] wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.<ref name=Coleman-2003/> Landau also developed a [[mean-field theory]] for continuous phase transitions, which described ordered phases as [[Spontaneous symmetry breaking|spontaneous breakdown of symmetry]]. The theory also introduced the notion of an [[order parameter]] to distinguish between ordered phases.<ref name=Kadanoff-2009>{{cite book|last=Kadanoff|first=Leo, P.|title=Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena|year=2009|publisher=The University of Chicago|url=http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf|access-date=2012-06-14|archive-date=2015-12-31|archive-url=https://web.archive.org/web/20151231215516/http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf|url-status=dead}}</ref> Eventually in 1956, [[John Bardeen]], [[Leon Cooper]] and [[Robert Schrieffer]] developed the so-called [[BCS theory]] of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by [[phonon]]s in the lattice can give rise to a bound state called a [[Cooper pair]].<ref name=coleman />
+The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of [[superconductivity]] and the [[Kondo effect]].<ref name=Coleman-2003>{{cite journal|last=Coleman|first=Piers|title=Many-Body Physics: Unfinished Revolution|journal=Annales Henri Poincaré|year=2003|volume=4|issue=2|doi=10.1007/s00023-003-0943-9|arxiv=cond-mat/0307004|bibcode= 2003AnHP....4..559C|pages=559–580|citeseerx=10.1.1.242.6214|s2cid=8171617}}</ref> After [[World War II]], several ideas from quantum field theory were applied to condensed matter problems. These included recognition of [[collective excitation]] modes of solids and the important notion of a quasiparticle. Soviet physicist [[Lev Landau]] used the idea for the [[Fermi liquid theory]] wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.<ref name=Coleman-2003/> Landau also developed a [[mean-field theory]] for continuous phase transitions, which described ordered phases as [[Spontaneous symmetry breaking|spontaneous breakdown of symmetry]]. The theory also introduced the notion of an [[order parameter]] to distinguish between ordered phases.<ref name=Kadanoff-2009>{{cite book|last=Kadanoff|first=Leo, P.|title=Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena|year=2009|publisher=The University of Chicago|url=http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf|access-date=2012-06-14|archive-date=2015-12-31|archive-url=https://web.archive.org/web/20151231215516/http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf}}</ref> Eventually in 1956, [[John Bardeen]], [[Leon Cooper]] and [[Robert Schrieffer]] developed the so-called [[BCS theory]] of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by [[phonon]]s in the lattice can give rise to a bound state called a [[Cooper pair]].<ref name=coleman />
 [[File:Quantum Hall effect - Russian.png|class=skin-invert-image|thumb|right|The [[quantum Hall effect]]: Components of the Hall resistivity as a function of the external magnetic field<ref name="von Klitzing"/>{{rp|fig. 14}}]]
 The study of phase transitions and the critical behavior of observables, termed [[critical phenomena]], was a major field of interest in the 1960s.<ref name=Fisher-rmp-1998>{{cite journal|last=Fisher|first=Michael E.|title=Renormalization group theory: Its basis and formulation in statistical physics|journal=Reviews of Modern Physics|year=1998|volume=70|issue=2|doi=10.1103/RevModPhys.70.653|bibcode= 1998RvMP...70..653F|pages=653–681|citeseerx=10.1.1.129.3194}}</ref> [[Leo Kadanoff]], [[Benjamin Widom]] and [[Michael Fisher]] developed the ideas of [[critical exponent]]s and [[widom scaling]]. These ideas were unified by [[Kenneth G. Wilson]] in 1972, under the formalism of the [[renormalization group]] in the context of quantum field theory.<ref name=Fisher-rmp-1998/>
-The [[quantum Hall effect]] was discovered by [[Klaus von Klitzing]], Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant <math>e^2/h</math>.(see figure) The effect was observed to be independent of parameters such as system size and impurities.<ref name="von Klitzing">{{cite web |url= https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-date=2022-10-09 |url-status=live |title= The Quantized Hall Effect |last= von Klitzing |first= Klaus |date= 9 Dec 1985 |website= Nobelprize.org}}</ref>  In 1981, theorist [[Robert Laughlin]] proposed a theory explaining the unanticipated precision of the integral plateau.  It also implied that the Hall conductance is proportional to a topological invariant, called [[Chern class#Chern numbers|Chern number]], whose relevance for the band structure of solids was formulated by [[David J. Thouless]] and collaborators.<ref name="Avron-hall-2003">{{cite journal|last=Avron|first=Joseph E. |author2=Osadchy, Daniel |author3=Seiler, Ruedi |title=A Topological Look at the Quantum Hall Effect|journal=Physics Today|year=2003|volume=56|issue=8|doi=10.1063/1.1611351|bibcode= 2003PhT....56h..38A|pages=38–42|doi-access=free}}</ref><ref name="Thouless1998">{{cite book|author=David J Thouless|title=Topological Quantum Numbers in Nonrelativistic Physics|date=12 March 1998|publisher=World Scientific|isbn=978-981-4498-03-6}}</ref>{{rp|69, 74}} Shortly after, in 1982, [[Horst Störmer]] and [[Daniel Tsui]] observed the [[fractional quantum Hall effect]] where the conductance was now a rational multiple of the constant <math>e^2/h</math>. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a [[variational method]] solution, named the [[Laughlin wavefunction]].<ref name=wen-1992>{{cite journal|last=Wen|first=Xiao-Gang|title=Theory of the edge states in fractional quantum Hall effects|journal=International Journal of Modern Physics C|year=1992|volume=6|issue=10|pages=1711–1762|url=http://dao.mit.edu/~wen/pub/edgere.pdf|access-date=14 June 2012|doi=10.1142/S0217979292000840|bibcode=1992IJMPB...6.1711W|citeseerx=10.1.1.455.2763|archive-url=https://web.archive.org/web/20050522083243/http://dao.mit.edu/%7Ewen/pub/edgere.pdf|archive-date=22 May 2005|url-status=dead}}</ref> The study of topological properties of the fractional Hall effect remains an active field of research.<ref name=":0">{{Cite book|last1=Girvin|first1=Steven M.|url=https://books.google.com/books?id=2ESIDwAAQBAJ|title=Modern Condensed Matter Physics|last2=Yang|first2=Kun|date=2019-02-28|publisher=Cambridge University Press|isbn=978-1-108-57347-4|language=en}}</ref> Decades later, the aforementioned topological band theory advanced by [[David J. Thouless]] and collaborators<ref>{{Cite journal|last1=Thouless|first1=D. J.|last2=Kohmoto|first2=M.|last3=Nightingale|first3=M. P.|last4=den Nijs|first4=M.|date=1982-08-09|title=Quantized Hall Conductance in a Two-Dimensional Periodic Potential|journal=Physical Review Letters|volume=49|issue=6|pages=405–408|doi=10.1103/PhysRevLett.49.405|bibcode=1982PhRvL..49..405T|doi-access=free}}</ref> was further expanded leading to the discovery of [[topological insulator]]s.<ref>{{Cite journal|last1=Kane|first1=C. L.|last2=Mele|first2=E. J.|date=2005-11-23|title=Quantum Spin Hall Effect in Graphene|url=https://link.aps.org/doi/10.1103/PhysRevLett.95.226801|journal=Physical Review Letters|volume=95|issue=22|pages=226801|doi=10.1103/PhysRevLett.95.226801|pmid=16384250|arxiv=cond-mat/0411737|bibcode=2005PhRvL..95v6801K|s2cid=6080059}}</ref><ref>{{Cite journal|last1=Hasan|first1=M. Z.|last2=Kane|first2=C. L.|date=2010-11-08|title=Colloquium: Topological insulators|url=https://link.aps.org/doi/10.1103/RevModPhys.82.3045|journal=Reviews of Modern Physics|volume=82|issue=4|pages=3045–3067|doi=10.1103/RevModPhys.82.3045|arxiv=1002.3895|bibcode=2010RvMP...82.3045H|s2cid=16066223}}</ref>
+The [[quantum Hall effect]] was discovered by [[Klaus von Klitzing]], Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant <math>e^2/h</math>.(see figure) The effect was observed to be independent of parameters such as system size and impurities.<ref name="von Klitzing">{{cite web |url= https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-date=2022-10-09 |url-status=live |title= The Quantized Hall Effect |last= von Klitzing |first= Klaus |date= 9 Dec 1985 |website= Nobelprize.org}}</ref>  In 1981, theorist [[Robert Laughlin]] proposed a theory explaining the unanticipated precision of the integral plateau.  It also implied that the Hall conductance is proportional to a topological invariant, called [[Chern class#Chern numbers|Chern number]], whose relevance for the band structure of solids was formulated by [[David J. Thouless]] and collaborators.<ref name="Avron-hall-2003">{{cite journal|last=Avron|first=Joseph E. |author2=Osadchy, Daniel |author3=Seiler, Ruedi |title=A Topological Look at the Quantum Hall Effect|journal=Physics Today|year=2003|volume=56|issue=8|doi=10.1063/1.1611351|bibcode= 2003PhT....56h..38A|pages=38–42|doi-access=free}}</ref><ref name="Thouless1998">{{cite book|author=David J Thouless|title=Topological Quantum Numbers in Nonrelativistic Physics|date=12 March 1998|publisher=World Scientific|isbn=978-981-4498-03-6}}</ref>{{rp|69, 74}} Shortly after, in 1982, [[Horst Störmer]] and [[Daniel Tsui]] observed the [[fractional quantum Hall effect]] where the conductance was now a rational multiple of the constant <math>e^2/h</math>. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a [[variational method]] solution, named the [[Laughlin wavefunction]].<ref name=wen-1992>{{cite journal|last=Wen|first=Xiao-Gang|title=Theory of the edge states in fractional quantum Hall effects|journal=International Journal of Modern Physics C|year=1992|volume=6|issue=10|pages=1711–1762|url=http://dao.mit.edu/~wen/pub/edgere.pdf|access-date=14 June 2012|doi=10.1142/S0217979292000840|bibcode=1992IJMPB...6.1711W|citeseerx=10.1.1.455.2763|archive-url=https://web.archive.org/web/20050522083243/http://dao.mit.edu/%7Ewen/pub/edgere.pdf|archive-date=22 May 2005}}</ref> The study of topological properties of the fractional Hall effect remains an active field of research.<ref name=":0">{{Cite book|last1=Girvin|first1=Steven M.|url=https://books.google.com/books?id=2ESIDwAAQBAJ|title=Modern Condensed Matter Physics|last2=Yang|first2=Kun|date=2019-02-28|publisher=Cambridge University Press|isbn=978-1-108-57347-4|language=en}}</ref> Decades later, the aforementioned topological band theory advanced by [[David J. Thouless]] and collaborators<ref>{{Cite journal|last1=Thouless|first1=D. J.|last2=Kohmoto|first2=M.|last3=Nightingale|first3=M. P.|last4=den Nijs|first4=M.|date=1982-08-09|title=Quantized Hall Conductance in a Two-Dimensional Periodic Potential|journal=Physical Review Letters|volume=49|issue=6|pages=405–408|doi=10.1103/PhysRevLett.49.405|bibcode=1982PhRvL..49..405T|doi-access=free}}</ref> was further expanded leading to the discovery of [[topological insulator]]s.<ref>{{Cite journal|last1=Kane|first1=C. L.|last2=Mele|first2=E. J.|date=2005-11-23|title=Quantum Spin Hall Effect in Graphene|url=https://link.aps.org/doi/10.1103/PhysRevLett.95.226801|journal=Physical Review Letters|volume=95|issue=22|article-number=226801|doi=10.1103/PhysRevLett.95.226801|pmid=16384250|arxiv=cond-mat/0411737|bibcode=2005PhRvL..95v6801K|s2cid=6080059}}</ref><ref>{{Cite journal|last1=Hasan|first1=M. Z.|last2=Kane|first2=C. L.|date=2010-11-08|title=Colloquium: Topological insulators|url=https://link.aps.org/doi/10.1103/RevModPhys.82.3045|journal=Reviews of Modern Physics|volume=82|issue=4|pages=3045–3067|doi=10.1103/RevModPhys.82.3045|arxiv=1002.3895|bibcode=2010RvMP...82.3045H|s2cid=16066223}}</ref>
 <!--
 A major revolution came in the field of [[crystallography]] with the discovery of [[quasicrystal]]s by [[Daniel Shechtman]]. In 1982 Shechtman observed that certain metallic [[alloy]]s produce unusual diffractograms that indicated that their crystalline structures are ordered, but lack [[translational symmetry]]. The discovery led the [[International Union of Crystallography]] to change its definition of a crystal to account for aperiodic structures.<ref name=bloomberg>{{cite news |url = https://www.bloomberg.com/news/2011-10-05/technion-s-shechtman-wins-chemistry-nobel-for-discovery-of-quasicrystals.html |title=Tecnion's Shechtman Wins Nobel in Chemistry for Quasicrystals Discovery |last = Gerlin |first = Andrea |date= 5 October 2011|work=Bloomberg}}</ref> The second half of the twentieth century was also important for the development of [[soft condensed matter]], in particular the [[thermodynamic equilibrium]] of several soft-matter systems such as polymers and liquid crystals due to [[Paul Flory|Flory]], [[Pierre de Gennes|de Gennes]] and others.<ref name=Cates-2004-soft>{{cite journal |last=Cates |first=M. E. |title=Soft Condensed Matter (Materia Condensata Soffice) |year=2004 |arxiv=cond-mat/0411650 |bibcode= 2004cond.mat.11650C |page = 11650 }}</ref> -->
-In 1986, [[Karl Alexander Müller|Karl Müller]] and [[Johannes Bednorz]] discovered the first [[high temperature superconductor]], La<sub>2-x</sub>Ba<sub>x</sub>CuO<sub>4</sub>,  which is superconducting at temperatures as high as 39 [[kelvin]].<ref> {{citation|author=Bednorz, J.G., Müller, K.A. |title=Possible high Tc superconductivity in the Ba−La−Cu−O system.|journal= Z. Physik B - Condensed Matter |volume=64 |pages=189–193|year=1986|issue=2 |doi=10.1007/BF01303701|bibcode=1986ZPhyB..64..189B }}</ref>   It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.<ref name="physics-world str-el">{{cite journal|last=Quintanilla|first=Jorge|author2=Hooley, Chris|title=The strong-correlations puzzle|journal=Physics World|volume=22|issue=6|pages=32|date=June 2009|url=http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|access-date=14 June 2012|url-status=dead|archive-url=https://web.archive.org/web/20120906002714/http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|archive-date=6 September 2012|bibcode=2009PhyW...22f..32Q|doi=10.1088/2058-7058/22/06/38}}</ref> A satisfactory theoretical description of high-temperature superconductors is still not known and the field of [[strongly correlated material]]s continues to be an active research topic.
+In 1986, [[Karl Alexander Müller|Karl Müller]] and [[Johannes Bednorz]] discovered the first [[high temperature superconductor]], La<sub>2-x</sub>Ba<sub>x</sub>CuO<sub>4</sub>,  which is superconducting at temperatures as high as 39 [[kelvin]].<ref>{{citation|author=Bednorz, J.G., Müller, K.A. |title=Possible high Tc superconductivity in the Ba−La−Cu−O system.|journal= Z. Physik B - Condensed Matter |volume=64 |pages=189–193|year=1986|issue=2 |doi=10.1007/BF01303701|bibcode=1986ZPhyB..64..189B }}</ref>   It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.<ref name="physics-world str-el">{{cite journal|last=Quintanilla|first=Jorge|author2=Hooley, Chris|title=The strong-correlations puzzle|journal=Physics World|volume=22|issue=6|page=32|date=June 2009|url=http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|access-date=14 June 2012|archive-url=https://web.archive.org/web/20120906002714/http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|archive-date=6 September 2012|bibcode=2009PhyW...22f..32Q|doi=10.1088/2058-7058/22/06/38}}</ref> A satisfactory theoretical description of high-temperature superconductors is still not known and the field of [[strongly correlated material]]s continues to be an active research topic.
 <!--
-The 1986 discovery of [[high temperature superconductivity]] generated interest in the study of [[strongly correlated materials]].<ref name=bouvier-2010>{{cite journal|last=Bouvier|first=Jacqueline|author2=Bok, Julien |title=Electron–Phonon Interaction in the High-T<sub>C</sub> Cuprates in the Framework of the Van Hove Scenario|journal=Advances in Condensed Matter Physics|year=2010|volume=2010|doi=10.1155/2010/472636|pages=472636}}</ref> Modern research in condensed matter physics is focused on problems in strongly correlated materials, [[quantum phase transitions]] and applications of [[quantum field theory]] to condensed matter systems. Problems of current interest include description of high temperature superconductivity, [[topological order]], and other novel materials such as [[graphene]] and [[carbon nanotube]]s.<ref name=yeh-perspective />
+The 1986 discovery of [[high temperature superconductivity]] generated interest in the study of [[strongly correlated materials]].<ref name=bouvier-2010>{{cite journal|last=Bouvier|first=Jacqueline|author2=Bok, Julien |title=Electron–Phonon Interaction in the High-T<sub>C</sub> Cuprates in the Framework of the Van Hove Scenario|journal=Advances in Condensed Matter Physics|year=2010|volume=2010|doi=10.1155/2010/472636|article-number=472636}}</ref> Modern research in condensed matter physics is focused on problems in strongly correlated materials, [[quantum phase transitions]] and applications of [[quantum field theory]] to condensed matter systems. Problems of current interest include description of high temperature superconductivity, [[topological order]], and other novel materials such as [[graphene]] and [[carbon nanotube]]s.<ref name=yeh-perspective />
 -->
-In 2012, several groups released preprints which suggest that [[Samarium#Samarium hexaboride|samarium hexaboride]] has the properties of a [[topological insulator]]<ref name="Nature-1">{{cite journal|journal=[[Nature (journal)|Nature]]|volume=492|issue=7428|pages=165|title=Hopes surface for exotic insulator|author=Eugenie Samuel Reich|doi=10.1038/492165a|pmid=23235853|year=2012|bibcode=2012Natur.492..165S|doi-access=free}}</ref> in accord with the earlier theoretical predictions.<ref name="TKI">{{Cite journal| doi= 10.1103/PhysRevLett.104.106408| pmid= 20366446| volume= 104| issue= 10| pages= 106408| last= Dzero| first= V.|author2=K. Sun |author3=V. Galitski |author4=P. Coleman |title= Topological Kondo Insulators| journal= Physical Review Letters| year= 2010|arxiv= 0912.3750 |bibcode= 2010PhRvL.104j6408D| s2cid= 119270507}}</ref> Since samarium hexaboride is an established [[Kondo insulator]], i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.
+In 2012, several groups released preprints which suggest that [[Samarium#Samarium hexaboride|samarium hexaboride]] has the properties of a [[topological insulator]]<ref name="Nature-1">{{cite journal|journal=[[Nature (journal)|Nature]]|volume=492|issue=7428|page=165|title=Hopes surface for exotic insulator|author=Eugenie Samuel Reich|doi=10.1038/492165a|pmid=23235853|year=2012|bibcode=2012Natur.492..165S|doi-access=free}}</ref> in accord with the earlier theoretical predictions.<ref name="TKI">{{Cite journal| doi= 10.1103/PhysRevLett.104.106408| pmid= 20366446| volume= 104| issue= 10| article-number= 106408| last= Dzero| first= V.|author2=K. Sun |author3=V. Galitski |author4=P. Coleman |title= Topological Kondo Insulators| journal= Physical Review Letters| year= 2010|arxiv= 0912.3750 |bibcode= 2010PhRvL.104j6408D| s2cid= 119270507}}</ref> Since samarium hexaboride is an established [[Kondo insulator]], i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.
 ==Theoretical==
@@ Line 66: / Line 66: @@
 {{Main|Electronic band structure}}
-The metallic state has historically been an important building block for studying properties of solids.<ref name="AshcroftMermin1976"/> The first theoretical description of metals was given by [[Paul Drude]] in 1900 with the [[Drude model]], which explained electrical and thermal properties by describing a metal as an [[ideal gas]] of then-newly discovered [[electron]]s.  He was able to derive the empirical [[Wiedemann-Franz law]] and get results in close agreement with the experiments.<ref name=Hoddeson-1992/>{{rp|90–91}}  This classical model was then improved by [[Arnold Sommerfeld]] who incorporated the [[Fermi–Dirac statistics]] of electrons and was able to explain the anomalous behavior of the [[specific heat]] of metals in the [[Wiedemann–Franz law]].<ref name=Hoddeson-1992/>{{rp|101–103}}  In 1912, The structure of crystalline solids was studied by [[Max von Laue]] and Paul Knipping, when they observed the [[X-ray diffraction]] pattern of crystals, and concluded that crystals get their structure from periodic [[lattice model (physics)|lattices]] of atoms.<ref name=Hoddeson-1992/>{{rp|48}}<ref>{{cite journal|last=Eckert|first=Michael|title=Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions|journal=Acta Crystallographica A|year=2011|volume=68|issue=1|doi=10.1107/S0108767311039985|pmid=22186281|url=http://journals.iucr.org/a/issues/2012/01/00/wx0005/index.html|bibcode= 2012AcCrA..68...30E|pages=30–39|doi-access=free}}</ref>  In 1928, Swiss physicist [[Felix Bloch]] provided a wave function solution to the [[Schrödinger equation]] with a [[Periodic function|periodic]] potential, known as [[Bloch's theorem]].<ref name=han-2010>{{cite book|last=Han|first=Jung Hoon|title=Solid State Physics|year=2010|publisher=Sung Kyun Kwan University|url=http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|url-status=dead|archive-url=https://web.archive.org/web/20130520224858/http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|archive-date=2013-05-20}}</ref>
+The metallic state has historically been an important building block for studying properties of solids.<ref name="AshcroftMermin1976"/> The first theoretical description of metals was given by [[Paul Drude]] in 1900 with the [[Drude model]], which explained electrical and thermal properties by describing a metal as an [[ideal gas]] of then-newly discovered [[electron]]s.  He was able to derive the empirical [[Wiedemann-Franz law]] and get results in close agreement with the experiments.<ref name=Hoddeson-1992/>{{rp|90–91}}  This classical model was then improved by [[Arnold Sommerfeld]] who incorporated the [[Fermi–Dirac statistics]] of electrons and was able to explain the anomalous behavior of the [[specific heat]] of metals in the [[Wiedemann–Franz law]].<ref name=Hoddeson-1992/>{{rp|101–103}}  In 1912, The structure of crystalline solids was studied by [[Max von Laue]] and Paul Knipping, when they observed the [[X-ray diffraction]] pattern of crystals, and concluded that crystals get their structure from periodic [[lattice model (physics)|lattices]] of atoms.<ref name=Hoddeson-1992/>{{rp|48}}<ref>{{cite journal|last=Eckert|first=Michael|title=Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions|journal=Acta Crystallographica A|year=2011|volume=68|issue=1|doi=10.1107/S0108767311039985|pmid=22186281|url=http://journals.iucr.org/a/issues/2012/01/00/wx0005/index.html|bibcode= 2012AcCrA..68...30E|pages=30–39|doi-access=free|url-access=subscription}}</ref>  In 1928, Swiss physicist [[Felix Bloch]] provided a wave function solution to the [[Schrödinger equation]] with a [[Periodic function|periodic]] potential, known as [[Bloch's theorem]].<ref name=han-2010>{{cite book|last=Han|first=Jung Hoon|title=Solid State Physics|year=2010|publisher=Sung Kyun Kwan University|url=http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|archive-url=https://web.archive.org/web/20130520224858/http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|archive-date=2013-05-20}}</ref>
 Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions.<ref name=perdew-2010>{{cite journal|last=Perdew|first=John P.|author2=Ruzsinszky, Adrienn|author2-link=Adrienn Ruzsinszky |title=Fourteen Easy Lessons in Density Functional Theory|journal=International Journal of Quantum Chemistry|year=2010|volume=110|pages=2801–2807|url=http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-date=2022-10-09 |url-status=live|access-date=13 May 2012|doi=10.1002/qua.22829|issue=15|doi-access=free}}</ref> The [[Thomas–Fermi model|Thomas–Fermi theory]], developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a [[Variational method|variational parameter]]. Later in the 1930s, [[Douglas Hartree]], [[Vladimir Fock]] and [[John C. Slater|John Slater]] developed the so-called [[Hartree–Fock method|Hartree–Fock wavefunction]] as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for [[Exchange symmetry|exchange statistics]] of single particle electron wavefunctions.  In general, it is very difficult to solve the Hartree–Fock equation.  Only the free electron gas case can be solved exactly.<ref name="AshcroftMermin1976">{{cite book|author1=Neil W. Ashcroft|author2=N. David Mermin|title=Solid state physics|year=1976|publisher=Saunders College|isbn=978-0-03-049346-1}}</ref>{{rp|330–337}} Finally in 1964–65, [[Walter Kohn]], [[Pierre Hohenberg]] and [[Lu Jeu Sham]] proposed the [[density functional theory]] (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.<ref name=perdew-2010 />
@@ Line 102: / Line 102: @@
 ===External magnetic fields===
-In experimental condensed matter physics, external [[magnetic field]]s act as [[thermodynamic variable]]s that control the state, phase transitions and properties of material systems.<ref name=iupap-report>{{cite web |last=Committee on Facilities for Condensed Matter Physics|title=Report of the IUPAP working group on Facilities for Condensed Matter Physics : High Magnetic Fields |url=http://archive.iupap.org/wg/wg3/hmff/file_50963.pdf |publisher=International Union of Pure and Applied Physics|year=2004 |quote=The magnetic field is not simply a spectroscopic tool but a thermodynamic variable which, along with temperature and pressure, controls the state, the phase transitions and the properties of materials.|access-date=2016-02-07|archive-url=https://web.archive.org/web/20140222151520/http://www.iupap.org/wg/wg3/hmff/file_50963.pdf|archive-date=2014-02-22|url-status=dead }}</ref>  [[Nuclear magnetic resonance]] (NMR) is a method by which external [[magnetic fields]] are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60 [[Tesla (unit)|tesla]].  Higher magnetic fields can improve the quality of NMR measurement data.<ref name="StatesAstronomy2013"/>{{rp|69}}<ref>{{cite book|title=High Magnetic Fields|chapter=Nuclear Magnetic Resonance in Solids at very high magnetic fields|author1=Moulton, W. G. |author2=Reyes, A. P. |editor=Herlach, Fritz |series=Science and Technology|publisher=World Scientific|year=2006|chapter-url=https://books.google.com/books?id=tN8CbCHzBmcC&pg=PA185|isbn=978-981-277-488-0}}</ref>{{rp|185}} [[Quantum oscillations]] is another experimental method where high magnetic fields are used to study material properties such as the geometry of the [[Fermi surface]].<ref name=doiron-leyraud2007>{{cite journal|last=Doiron-Leyraud|first=Nicolas|title=Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor|journal=Nature|year=2007|volume=447|pages=565–568|doi=10.1038/nature05872|arxiv= 0801.1281 |bibcode= 2007Natur.447..565D|issue=7144|pmid=17538614 |s2cid=4397560|display-authors=etal}}</ref>  High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized [[magnetoelectric effect]], image [[magnetic monopole]], and the half-integer [[quantum Hall effect]].<ref name="StatesAstronomy2013">{{cite book|author=Committee to Assess the Current Status and Future Direction of High Magnetic Field Science in the United States; Board on Physics and Astronomy; Division on Engineering and Physical Sciences; National Research Council|title=High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions|url=http://www.nap.edu/catalog/18355/high-magnetic-field-science-and-its-application-in-the-united-states|date=25 November 2013|publisher=National Academies Press|isbn=978-0-309-28634-3|doi=10.17226/18355}}</ref>{{rp|57}}
+In experimental condensed matter physics, external [[magnetic field]]s act as [[thermodynamic variable|thermodynamic variables]] that control the state, phase transitions and properties of material systems.<ref name=iupap-report>{{cite web |last=Committee on Facilities for Condensed Matter Physics|title=Report of the IUPAP working group on Facilities for Condensed Matter Physics: High Magnetic Fields |url=http://archive.iupap.org/wg/wg3/hmff/file_50963.pdf |publisher=International Union of Pure and Applied Physics|year=2004 |quote=The magnetic field is not simply a spectroscopic tool but a thermodynamic variable which, along with temperature and pressure, controls the state, the phase transitions and the properties of materials.|access-date=2016-02-07|archive-url=https://web.archive.org/web/20140222151520/http://www.iupap.org/wg/wg3/hmff/file_50963.pdf|archive-date=2014-02-22}}</ref>  [[Nuclear magnetic resonance]] (NMR) is a method by which external [[magnetic fields]] are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60 [[Tesla (unit)|tesla]].  Higher magnetic fields can improve the quality of NMR measurement data.<ref name="StatesAstronomy2013"/>{{rp|69}}<ref>{{cite book|title=High Magnetic Fields|chapter=Nuclear Magnetic Resonance in Solids at very high magnetic fields|author1=Moulton, W. G. |author2=Reyes, A. P. |editor=Herlach, Fritz |series=Science and Technology|publisher=World Scientific|year=2006|chapter-url=https://books.google.com/books?id=tN8CbCHzBmcC&pg=PA185|isbn=978-981-277-488-0}}</ref>{{rp|185}} [[Quantum oscillations]] is another experimental method where high magnetic fields are used to study material properties such as the geometry of the [[Fermi surface]].<ref name=doiron-leyraud2007>{{cite journal|last=Doiron-Leyraud|first=Nicolas|title=Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor|journal=Nature|year=2007|volume=447|pages=565–568|doi=10.1038/nature05872|arxiv= 0801.1281 |bibcode= 2007Natur.447..565D|issue=7144|pmid=17538614 |s2cid=4397560|display-authors=etal}}</ref>  High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized [[magnetoelectric effect]], image [[magnetic monopole]], and the half-integer [[quantum Hall effect]].<ref name="StatesAstronomy2013">{{cite book|author=Committee to Assess the Current Status and Future Direction of High Magnetic Field Science in the United States; Board on Physics and Astronomy; Division on Engineering and Physical Sciences; National Research Council|title=High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions|url=http://www.nap.edu/catalog/18355/high-magnetic-field-science-and-its-application-in-the-united-states|date=25 November 2013|publisher=National Academies Press|isbn=978-0-309-28634-3|doi=10.17226/18355}}</ref>{{rp|57}}
 ===Magnetic resonance spectroscopy===
@@ Line 119: / Line 119: @@
 [[File:Fullerene Nanogears - GPN-2000-001535.jpg|thumb|right|Computer simulation of ''nanogears'' made of [[fullerene]] molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.]]
-Research in condensed matter physics<ref name=":0" /><ref>{{cite book|url=https://www.cambridge.org/core/books/introduction-to-manybody-physics/B7598FC1FCEE0285F5EC767E835854C8|title=Introduction to Many-Body Physics|last=Coleman|first=Piers|date=2015|publisher=Cambridge Core|doi=10.1017/CBO9781139020916 |isbn=9780521864886 |language=en|access-date=2020-04-20}}</ref> has given rise to several device applications, such as the development of the [[semiconductor]] [[transistor]],<ref name=marvincohen2008 /> [[laser]] technology,<ref name=NRC1986 /> [[magnetic storage]], [[liquid crystals]], [[optical fibres]]<ref>{{cite web|title=Condensed Matter|url=https://live-sas-physics.pantheon.sas.upenn.edu/research/condensed-matter|website=Physics Pantheon|access-date=2023-11-30}}</ref> and several phenomena studied in the context of [[nanotechnology]].<ref name="2010Committee2007">{{cite book|author=Committee on CMMP 2010; Solid State Sciences Committee; Board on Physics and Astronomy; Division on Engineering and Physical Sciences, National Research Council|title=Condensed-Matter and Materials Physics: The Science of the World Around Us|url=http://www.nap.edu/catalog/11967/condensed-matter-and-materials-physics-the-science-of-the-world|date=21 December 2007|publisher=National Academies Press|isbn=978-0-309-13409-5|doi=10.17226/11967}}</ref>{{rp|111ff}} Methods such as [[Scanning tunneling microscope|scanning-tunneling microscopy]] can be used to control processes at the [[nanometer]] scale, and have given rise to the study of nanofabrication.<ref name=yeh-perspective>{{cite journal |last=Yeh|first=Nai-Chang |title=A Perspective of Frontiers in Modern Condensed Matter Physics |journal=AAPPS Bulletin|year=2008|volume=18|issue=2 |url = https://yehgroup.caltech.edu/files/2016/08/AAPPS_v18_no2_pg11.pdf |access-date=19 June 2018}}</ref> Such molecular machines were developed for example by Nobel laureates in chemistry [[Ben Feringa]], [[Jean-Pierre Sauvage]] and [[Fraser Stoddart]]. Feringa and his team developed multiple molecular machines such as the [[molecular car]], molecular windmill and many more.<ref>{{Cite journal |last1=Kudernac |first1=Tibor |last2=Ruangsupapichat |first2=Nopporn |last3=Parschau |first3=Manfred |last4=Maciá |first4=Beatriz |last5=Katsonis |first5=Nathalie |last6=Harutyunyan |first6=Syuzanna R. |last7=Ernst |first7=Karl-Heinz |last8=Feringa |first8=Ben L. |date=2011-11-01 |title=Electrically driven directional motion of a four-wheeled molecule on a metal surface |url=https://www.nature.com/articles/nature10587 |journal=Nature |language=en |volume=479 |issue=7372 |pages=208–211 |doi=10.1038/nature10587 |pmid=22071765 |bibcode=2011Natur.479..208K |s2cid=6175720 |issn=1476-4687|url-access=subscription }}</ref>
+Research in condensed matter physics<ref name=":0" /><ref>{{cite book|url=https://www.cambridge.org/core/books/introduction-to-manybody-physics/B7598FC1FCEE0285F5EC767E835854C8|title=Introduction to Many-Body Physics|last=Coleman|first=Piers|date=2015|publisher=Cambridge Core|doi=10.1017/CBO9781139020916 |isbn=978-0-521-86488-6 |language=en|access-date=2020-04-20}}</ref> has given rise to several device applications, such as the development of the [[semiconductor]] [[transistor]],<ref name=marvincohen2008 /> [[laser]] technology,<ref name=NRC1986 /> [[magnetic storage]], [[liquid crystals]], [[optical fibres]]<ref>{{cite web|title=Condensed Matter|url=https://live-sas-physics.pantheon.sas.upenn.edu/research/condensed-matter|website=Physics Pantheon|access-date=2023-11-30}}</ref> and several phenomena studied in the context of [[nanotechnology]].<ref name="2010Committee2007">{{cite book|author=Committee on CMMP 2010; Solid State Sciences Committee; Board on Physics and Astronomy; Division on Engineering and Physical Sciences, National Research Council|title=Condensed-Matter and Materials Physics: The Science of the World Around Us|url=http://www.nap.edu/catalog/11967/condensed-matter-and-materials-physics-the-science-of-the-world|date=21 December 2007|publisher=National Academies Press|isbn=978-0-309-13409-5|doi=10.17226/11967}}</ref>{{rp|111ff}} Methods such as [[Scanning tunneling microscope|scanning-tunneling microscopy]] can be used to control processes at the [[nanometer]] scale, and have given rise to the study of nanofabrication.<ref name=yeh-perspective>{{cite journal |last=Yeh|first=Nai-Chang |title=A Perspective of Frontiers in Modern Condensed Matter Physics |journal=AAPPS Bulletin|year=2008|volume=18|issue=2 |url = https://yehgroup.caltech.edu/files/2016/08/AAPPS_v18_no2_pg11.pdf |access-date=19 June 2018}}</ref> Such molecular machines were developed for example by Nobel laureates in chemistry [[Ben Feringa]], [[Jean-Pierre Sauvage]] and [[Fraser Stoddart]]. Feringa and his team developed multiple molecular machines such as the [[molecular car]], molecular windmill and many more.<ref>{{Cite journal |last1=Kudernac |first1=Tibor |last2=Ruangsupapichat |first2=Nopporn |last3=Parschau |first3=Manfred |last4=Maciá |first4=Beatriz |last5=Katsonis |first5=Nathalie |last6=Harutyunyan |first6=Syuzanna R. |last7=Ernst |first7=Karl-Heinz |last8=Feringa |first8=Ben L. |date=2011-11-01 |title=Electrically driven directional motion of a four-wheeled molecule on a metal surface |url=https://www.nature.com/articles/nature10587 |journal=Nature |language=en |volume=479 |issue=7372 |pages=208–211 |doi=10.1038/nature10587 |pmid=22071765 |bibcode=2011Natur.479..208K |s2cid=6175720 |issn=1476-4687|url-access=subscription }}</ref>
 In [[quantum computation]], information is represented by quantum bits, or [[qubit]]s. The qubits may [[quantum decoherence|decohere]] quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, including [[Josephson junction]] qubits, [[spintronic]] qubits using the [[Spin (physics)|spin]] orientation of magnetic materials, and the topological non-Abelian [[anyon]]s from [[fractional quantum Hall effect]] states.<ref name=yeh-perspective />

Condensed matter physics: Difference between revisions

Latest revision as of 00:07, 17 October 2025

Contents

Etymology

History

Classical physics

Advent of quantum mechanics

Modern many-body physics

Theoretical

Emergence

Electronic theory of solids

Symmetry breaking

Phase transition

Experimental

Scattering

External magnetic fields

Magnetic resonance spectroscopy

Cold atomic gases

Applications

See also

Notes

References

Further reading

External links

Navigation menu

Condensed matter physics: Difference between revisions

Latest revision as of 00:07, 17 October 2025

Etymology

History

Classical physics

Advent of quantum mechanics

Modern many-body physics

Theoretical

Emergence

Electronic theory of solids

Symmetry breaking

Phase transition

Experimental

Scattering

External magnetic fields

Magnetic resonance spectroscopy

Cold atomic gases

Applications

See also

Notes

References

Further reading

External links

Navigation menu

Search