Condensed matter physics

Last updated

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the constituents are strong. The most familiar examples of condensed phases are solids and liquids, which arise from the electromagnetic forces between atoms. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics, electromagnetism and statistical mechanics.


More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. The study of condensed matter physics involves measuring various material properties via experimental probes along with using methods of theoretical physics to develop mathematical models that help in understanding physical behavior.

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, [1] and the Division of Condensed Matter Physics is the largest division at the American Physical Society. [2] The field overlaps with chemistry, materials science, 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. [3]

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 new, related specialty of condensed matter physics. [4] According to physicist Philip Warren Anderson, the term 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, [5] as they felt it did not exclude their interests in the study of liquids, nuclear matter, and so on. [6] Although Anderson and Heine helped popularize the name "condensed matter", it had been present in Europe for some years, most prominently in the form of a journal published in English, French, and German by Springer-Verlag titled Physics of Condensed Matter, which was launched in 1963. [7] The funding environment and Cold War politics of the 1960s and 1970s were also factors that lead some physicists to prefer the name "condensed matter physics", which emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, over "solid state physics", which was often associated with the industrial applications of metals and semiconductors. [8] The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics. [4]

References to "condensed" state can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids, [9] 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 bodies'".

History of classical physics

Classical physics

Heike Kamerlingh Onnes and Johannes van der Waals with the helium liquefactor at Leiden in 1908 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. [10] 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. [11] [note 1]

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. [10] 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, [13] 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. [14] :35–38 By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively. [10]

Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. [3] 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. [15] [16] :27–29 However, despite the success of Drude's free electron 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. [17] :366–368

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. [18] The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades. [19] 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." [20]

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. [17] :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. [21] Band structure calculations was 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. [3]

A replica of the first point-contact transistor in Bell labs 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 a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. [22] 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, since 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 the theoretical explanation for the quantum Hall effect discovered half a century later. [23] :458–460 [24]

Magnetism as a property of matter has been known in China since 4000 BC. [25] :1–2 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. [26] Pierre Curie studied the dependence of magnetization on temperature and discovered the Curie point phase transition in ferromagnetic materials. [25] In 1906, Pierre Weiss introduced the concept of magnetic domains to explain the main properties of ferromagnets. [27] :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 spins that collectively acquired magnetization. [25] The Ising model was solved exactly to show that spontaneous magnetization cannot occur in one dimension but 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. [25] :36–38,g48

Modern many-body physics

A magnet levitating above a high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence. Meissner effect p1390048.jpg
A magnet levitating above a high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.

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. [29] 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. Russian 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. [29] 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. [30] Eventually in 1965, John Bardeen, Leon Cooper and John 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. [31]

The quantum Hall effect: Components of the Hall resistivity as a function of the external magnetic field Quantum Hall effect - Russian.png
The quantum Hall effect: Components of the Hall resistivity as a function of the external magnetic field

The study of phase transition and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s. [33] 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. [33]

The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductance to be integer multiples of a fundamental constant .(see figure) The effect was observed to be independent of parameters such as system size and impurities. [32] In 1981, theorist Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance can be characterized in terms of a topological invariable called Chern number. [34] [35] :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 a constant. 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. [36] The study of topological properties of the fractional Hall effect remains an active field of research.

In 1986, Karl Müller and Johannes Bednorz discovered the first high temperature superconductor, a material which was superconducting at temperatures as high as 50 kelvins. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role. [37] 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 2009, David Field and researchers at Aarhus University discovered spontaneous electric fields when creating prosaic films [ clarification needed ] of various gases. This has more recently expanded to form the research area of spontelectrics. [38]

In 2012 several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator [39] in accord with the earlier theoretical predictions. [40] Since samarium hexaboride is an established Kondo insulator, i.e. a strongly correlated electron material, the existence of a topological surface state in this material would lead to a topological insulator with strong electronic correlations.


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.


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. [31] 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. [41] Similarly, models of condensed matter systems have been studied where collective excitations behave like photons and electrons, thereby describing electromagnetism as an emergent phenomenon. [42] Emergent properties can also occur at the interface between materials: one example is the lanthanum aluminate-strontium titanate interface, where two non-magnetic insulators are joined to create conductivity, superconductivity, and ferromagnetism.

Electronic theory of solids

The metallic state has historically been an important building block for studying properties of solids. [43] 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. [16] :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. [16] :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 lattices of atoms. [16] :48 [44] In 1928, Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, called the Bloch wave. [45]

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. [46] 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's very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly. [43] :330–337 Finally in 1964–65, Walter Kohn, Pierre Hohenberg and Lu Jeu Sham proposed the density functional theory which gave realistic descriptions for bulk and surface properties of metals. The density functional theory (DFT) has been widely used since the 1970s for band structure calculations of variety of solids. [46]

Symmetry breaking

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. [47] [48]

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. [49]

Phase transition

Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as temperature. Classical phase transition occurs at finite temperature when the order of the system was destroyed. For example, when ice melts and becomes water, the ordered crystal structure is destroyed.

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. [50]

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. [50] 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. [51] :75ff

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. [52] :8–11

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. [51] :11


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. [53] 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.

Image of X-ray diffraction pattern from a protein crystal. Lysozym diffraction.png
Image of X-ray diffraction pattern from a protein crystal.


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 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. [54] :33–34

Neutrons can also probe atomic length scales and are used to study 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. [54] :33–34 [55] :39–43 Similarly, positron annihilation can be used as an indirect measurement of local electron density. [56] 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. [51] :258–259

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. [57] Nuclear magnetic resonance (NMR) is a method by which external magnetic fields are used to find resonance modes of individual electrons, thus giving information about the atomic, molecular, and bond structure of their neighborhood. 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. [58] :69 [59] :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. [60] High magnetic fields will be useful in experimentally testing of the various theoretical predictions such as the quantized magnetoelectric effect, image magnetic monopole, and the half-integer quantum Hall effect. [58] :57

Nuclear spectroscopy

The local structure, the structure of the nearest neighbour atoms, of condensed matter can be investigated with methods of nuclear spectroscopy, which are very sensitive to small changes. Using specific and radioactive nuclei, the nucleus becomes the probe that interacts with its sourrounding electric and magnetic fields (hyperfine interactions). The methods are suitable to study defects, diffusion, phase change, magnetism. Common methods are e.g. NMR, Mössbauer spectroscopy, or perturbed angular correlation (PAC). Especially PAC is ideal for the study of phase changes at extreme temperature above 2000°C due to no temperature dependence of the method.

Cold atomic gases

The first Bose-Einstein condensate observed in a gas of ultracold rubidium atoms. The blue and white areas represent higher density. 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. [61] 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. [62] [63]

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. [64]


Computer simulation of nanogears made of fullerene molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale. 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 has given rise to several device applications, such as the development of the semiconductor transistor, [3] laser technology, [51] and several phenomena studied in the context of nanotechnology. [65] :111ff 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. [66]

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, or the topological non-Abelian anyons from fractional quantum Hall effect states. [66]

Condensed matter physics also has important uses for biophysics, for example, the experimental method of magnetic resonance imaging, which is widely used in medical diagnosis. [66]

See also


  1. 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 [12] that a state metallic hydrogen exists at sufficiently high pressures (over 25 GPa), but this has not yet been observed.

Related Research Articles

BCS theory or Bardeen–Cooper–Schrieffer theory is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus.

Superconductivity electrical conductivity with almost zero resistance

Superconductivity is the set of physical properties observed in certain materials, wherein electrical resistance vanishes and from which magnetic flux fields are expelled. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

Phase transition transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma

The term phase transition is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.

High-temperature superconductivity Superconductive behavior at temperatures much higher than absolute zero

High-temperature superconductors are materials that behave as superconductors at temperatures above nearly -200°C (-320°F). This is the lowest temperature reachable by liquid nitrogen, one of the simplest coolant in cryogenics. All superconducting materials known at ordinary pressures currently work far below ambient temperatures and therefore require cooling. The majority of high-temperature superconductors are ceramics materials. On the other hand, Metallic superconductors usually work below -200°C: they are then called low-temperature superconductors. Metallic superconductors are also ordinary superconductors, since they were discovered and used before the high-temperature ones.

Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors.

A room-temperature superconductor is a material that is capable of exhibiting superconductivity at operating temperatures above 0 °C (273 K; 32 °F). While this is not strictly "room temperature", which would be approximately 20–25 °C (68–77 °F), it is the temperature at which ice forms, and can be reached and easily maintained in an everyday environment. As of 2019 the material with the highest accepted superconducting temperature is highly pressurized lanthanum decahydride (LaH10), whose transition temperature is 250 K (−23 °C). Previously the record was held by hydrogen sulfide, which has demonstrated superconductivity under high pressure at temperatures as high as 203 K (−70 °C). By substituting a small part of sulfur in the latter with phosphorus and using even higher pressures, it has been predicted that it might be possible to raise the critical temperature to above 0 °C and achieve room-temperature superconductivity. At atmospheric pressure the record is still held by the cuprates, which have demonstrated superconductivity at temperatures as high as 138 K (−135 °C).

In condensed matter physics, a Cooper pair or BCS pair is a pair of electrons bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper. Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the Fermi energy, which implies that the pair is bound. In conventional superconductors, this attraction is due to the electron–phonon interaction. The Cooper pair state is responsible for superconductivity, as described in the BCS theory developed by John Bardeen, Leon Cooper, and John Schrieffer for which they shared the 1972 Nobel Prize.

Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics.

Color superconductivity is a phenomenon predicted to occur in quark matter if the baryon density is sufficiently high (well above nuclear density) and the temperature is not too high (well below 1012 kelvin). Color superconducting phases are to be contrasted with the normal phase of quark matter, which is just a weakly interacting Fermi liquid of quarks.

Alexander Kuzemsky Russian physicist

Alexander Leonidovich Kuzemsky is a Russian theoretical physicist.

A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning and electrostatic interactions likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below.

In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, they are sometimes referred to as heavy electrons. Heavy fermion materials have a low-temperature specific heat whose linear term is up to 1000 times larger than the value expected from the free electron model. The properties of the heavy fermion compounds often derive from the partly filled f-orbitals of rare-earth or actinide ions, which behave like localized magnetic moments. The name "heavy fermion" comes from the fact that the fermion behaves as if it has an effective mass greater than its rest mass. In the case of electrons, below a characteristic temperature (typically 10 K), the conduction electrons in these metallic compounds behave as if they had an effective mass up to 1000 times the free particle mass. This large effective mass is also reflected in a large contribution to the resistivity from electron-electron scattering via the Kadowaki–Woods ratio. Heavy fermion behavior has been found in a broad variety of states including metallic, superconducting, insulating and magnetic states. Characteristic examples are CeCu6, CeAl3, CeCu2Si2, YbAl3, UBe13 and UPt3.

Subir Sachdev is Herchel Smith Professor of Physics at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, and received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018.

Piers Coleman British-American physicist

Piers Coleman is a British-born theoretical physicist, working in the field of theoretical condensed matter physics. Coleman is Professor of Physics at Rutgers University in New Jersey and at Royal Holloway, University of London.

In condensed matter physics, a quantum spin liquid is an unusual phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entanglement, fractionalized excitations, and absence of ordinary magnetic order.

Shoucheng Zhang Chinese American physicist

Shoucheng Zhang was a Chinese-American physicist who was the JG Jackson and CJ Wood professor of physics at Stanford University. He was a condensed matter theorist known for his work on topological insulators, the quantum Hall effect, the quantum spin Hall effect, spintronics, and high-temperature superconductivity. According to the National Academy of Science:

He discovered a new state of matter called topological insulator in which electrons can conduct along the edge without dissipation, enabling a new generation of electronic devices with much lower power consumption. For this ground breaking work he received numerous international awards, including the Buckley Prize, the Dirac Medal and Prize, the Europhysics Prize, the Physics Frontiers Prize and the Benjamin Franklin Medal.

In condensed matter physics, the resonating valence bond theory (RVB) is a theoretical model that attempts to describe high temperature superconductivity, and in particular the superconductivity in cuprate compounds. It was first proposed by an American physicist P. W. Anderson and Indian theoretical physicist Ganapathy Baskaran in 1987. The theory states that in copper oxide lattices, electrons from neighboring copper atoms interact to form a valence bond, which locks them in place. However, with doping, these electrons can act as mobile Cooper pairs and are able to superconduct. Anderson observed in his 1987 paper that the origins of superconductivity in doped cuprates was in the Mott insulator nature of crystalline copper oxide. RVB builds on the Hubbard and t-J models used in the study of strongly correlated materials.

Elihu Abrahams was a theoretical physicist, specializing in condensed matter physics. He is mostly notable for his work on electron transport in disordered systems.

Eduardo Hector Fradkin is an Argentinian-American theoretical physicist known for working in various areas of condensed matter physics, primarily using quantum field theoretical approaches. He is a Donald Biggar Willett Professor of Physics at the University of Illinois at Urbana–Champaign, where he is the director of the Institute for Condensed Matter Theory, and is the author of the book Field Theories of Condensed Matter Physics.

Several hundred metals, compounds, alloys and ceramics possess the property of superconductivity at low temperatures. The SU(2) color quark matter adjoins the list of superconducting systems. Although it is a mathematical abstraction, its properties are believed to be closely related to the SU(3) color quark matter, which exists in nature when ordinary matter is compressed at supranuclear densities above ~ 0.5 1039 nucleon/cm3.


  1. "Condensed Matter Physics Jobs: Careers in Condensed Matter Physics". Physics Today Jobs. Archived from the original on 2009-03-27. Retrieved 2010-11-01.
  2. "History of Condensed Matter Physics". American Physical Society. Retrieved 27 March 2012.
  3. 1 2 3 4 Cohen, Marvin L. (2008). "Essay: Fifty Years of Condensed Matter Physics". Physical Review Letters. 101 (25): 250001. Bibcode:2008PhRvL.101y0001C. doi:10.1103/PhysRevLett.101.250001. PMID   19113681 . Retrieved 31 March 2012.
  4. 1 2 Kohn, W. (1999). "An essay on condensed matter physics in the twentieth century" (PDF). Reviews of Modern Physics. 71 (2): S59–S77. Bibcode:1999RvMPS..71...59K. doi:10.1103/RevModPhys.71.S59. Archived from the original (PDF) on 25 August 2013. Retrieved 27 March 2012.
  5. "Philip Anderson". Department of Physics. Princeton University. Retrieved 27 March 2012.
  6. Anderson, Philip W. (November 2011). "In Focus: More and Different". World Scientific Newsletter. 33: 2.
  7. "Physics of Condensed Matter". 1963. Retrieved 20 April 2015.
  8. Martin, Joseph D. (2015). "What's in a Name Change? Solid State Physics, Condensed Matter Physics, and Materials Science" (PDF). Physics in Perspective. 17 (1): 3–32. Bibcode:2015PhP....17....3M. doi:10.1007/s00016-014-0151-7.
  9. Frenkel, J. (1947). Kinetic Theory of Liquids. Oxford University Press.
  10. 1 2 3 Goodstein, David; Goodstein, Judith (2000). "Richard Feynman and the History of Superconductivity" (PDF). Physics in Perspective. 2 (1): 30. Bibcode:2000PhP.....2...30G. doi:10.1007/s000160050035 . Retrieved 7 April 2012.
  11. Davy, John, ed. (1839). The collected works of Sir Humphry Davy: Vol. II. Smith Elder & Co., Cornhill.
  12. Silvera, Isaac F.; Cole, John W. (2010). "Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist". Journal of Physics. 215 (1): 012194. Bibcode:2010JPhCS.215a2194S. doi:10.1088/1742-6596/215/1/012194.
  13. Rowlinson, J. S. (1969). "Thomas Andrews and the Critical Point". Nature. 224 (8): 541–543. Bibcode:1969Natur.224..541R. doi:10.1038/224541a0.
  14. Atkins, Peter; de Paula, Julio (2009). Elements of Physical Chemistry. Oxford University Press. ISBN   978-1-4292-1813-9.
  15. Kittel, Charles (1996). Introduction to Solid State Physics. John Wiley & Sons. ISBN   978-0-471-11181-8.
  16. 1 2 3 4 Hoddeson, Lillian (1992). Out of the Crystal Maze: Chapters from The History of Solid State Physics. Oxford University Press. ISBN   978-0-19-505329-6.
  17. 1 2 Kragh, Helge (2002). Quantum Generations: A History of Physics in the Twentieth Century (Reprint ed.). Princeton University Press. ISBN   978-0-691-09552-3.
  18. van Delft, Dirk; Kes, Peter (September 2010). "The discovery of superconductivity" (PDF). Physics Today. 63 (9): 38–43. Bibcode:2010PhT....63i..38V. doi:10.1063/1.3490499 . Retrieved 7 April 2012.
  19. Slichter, Charles. "Introduction to the History of Superconductivity". Moments of Discovery. American Institute of Physics. Retrieved 13 June 2012.
  20. Schmalian, Joerg (2010). "Failed theories of superconductivity". Modern Physics Letters B. 24 (27): 2679–2691. arXiv: 1008.0447 . Bibcode:2010MPLB...24.2679S. doi:10.1142/S0217984910025280.
  21. Aroyo, Mois, I.; Müller, Ulrich; Wondratschek, Hans (2006). Historical introduction (PDF). International Tables for Crystallography. A. pp. 2–5. CiteSeerX . doi:10.1107/97809553602060000537. ISBN   978-1-4020-2355-2.
  22. Hall, Edwin (1879). "On a New Action of the Magnet on Electric Currents". American Journal of Mathematics. 2 (3): 287–92. doi:10.2307/2369245. JSTOR   2369245. Archived from the original on 2007-02-08. Retrieved 2008-02-28.
  23. Landau, L. D.; Lifshitz, E. M. (1977). Quantum Mechanics: Nonrelativistic Theory. Pergamon Press. ISBN   978-0-7506-3539-4.
  24. Lindley, David (2015-05-15). "Focus: Landmarks—Accidental Discovery Leads to Calibration Standard". Physics. 8. Archived from the original on 2015-09-07. Retrieved 2016-01-09.
  25. 1 2 3 4 Mattis, Daniel (2006). The Theory of Magnetism Made Simple. World Scientific. ISBN   978-981-238-671-7.
  26. Chatterjee, Sabyasachi (August 2004). "Heisenberg and Ferromagnetism". Resonance. 9 (8): 57–66. doi:10.1007/BF02837578 . Retrieved 13 June 2012.
  27. Visintin, Augusto (1994). Differential Models of Hysteresis. Springer. ISBN   978-3-540-54793-8.
  28. Merali, Zeeya (2011). "Collaborative physics: string theory finds a bench mate". Nature. 478 (7369): 302–304. Bibcode:2011Natur.478..302M. doi:10.1038/478302a. PMID   22012369.
  29. 1 2 Coleman, Piers (2003). "Many-Body Physics: Unfinished Revolution". Annales Henri Poincaré. 4 (2): 559–580. arXiv: cond-mat/0307004 . Bibcode:2003AnHP....4..559C. CiteSeerX . doi:10.1007/s00023-003-0943-9.
  30. Kadanoff, Leo, P. (2009). Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena (PDF). The University of Chicago.
  31. 1 2 Coleman, Piers (2016). Introduction to Many Body Physics. Cambridge University Press. ISBN   978-0-521-86488-6.
  32. 1 2 von Klitzing, Klaus (9 Dec 1985). "The Quantized Hall Effect" (PDF).
  33. 1 2 Fisher, Michael E. (1998). "Renormalization group theory: Its basis and formulation in statistical physics". Reviews of Modern Physics. 70 (2): 653–681. Bibcode:1998RvMP...70..653F. CiteSeerX . doi:10.1103/RevModPhys.70.653.
  34. Avron, Joseph E.; Osadchy, Daniel; Seiler, Ruedi (2003). "A Topological Look at the Quantum Hall Effect". Physics Today. 56 (8): 38–42. Bibcode:2003PhT....56h..38A. doi:10.1063/1.1611351.
  35. David J Thouless (12 March 1998). Topological Quantum Numbers in Nonrelativistic Physics. World Scientific. ISBN   978-981-4498-03-6.
  36. Wen, Xiao-Gang (1992). "Theory of the edge states in fractional quantum Hall effects" (PDF). International Journal of Modern Physics C. 6 (10): 1711–1762. Bibcode:1992IJMPB...6.1711W. CiteSeerX . doi:10.1142/S0217979292000840. Archived from the original (PDF) on 22 May 2005. Retrieved 14 June 2012.
  37. Quintanilla, Jorge; Hooley, Chris (June 2009). "The strong-correlations puzzle" (PDF). Physics World. 22 (6): 32. Bibcode:2009PhyW...22f..32Q. doi:10.1088/2058-7058/22/06/38. Archived from the original (PDF) on 6 September 2012. Retrieved 14 June 2012.
  38. Field, David; Plekan, O.; Cassidy, A.; Balog, R.; Jones, N.C. and Dunger, J. (12 Mar 2013). "Spontaneous electric fields in solid films: spontelectrics". Int.Rev.Phys.Chem. 32 (3): 345–392. doi:10.1080/0144235X.2013.767109.CS1 maint: multiple names: authors list (link)
  39. Eugenie Samuel Reich (2012). "Hopes surface for exotic insulator". Nature . 492 (7428): 165. Bibcode:2012Natur.492..165S. doi:10.1038/492165a. PMID   23235853.
  40. Dzero, V.; K. Sun; V. Galitski; P. Coleman (2010). "Topological Kondo Insulators". Physical Review Letters. 104 (10): 106408. arXiv: 0912.3750 . Bibcode:2010PhRvL.104j6408D. doi:10.1103/PhysRevLett.104.106408. PMID   20366446.
  41. "Understanding Emergence". National Science Foundation. Retrieved 30 March 2012.
  42. Levin, Michael; Wen, Xiao-Gang (2005). "Colloquium: Photons and electrons as emergent phenomena". Reviews of Modern Physics. 77 (3): 871–879. arXiv: cond-mat/0407140 . Bibcode:2005RvMP...77..871L. doi:10.1103/RevModPhys.77.871.
  43. 1 2 Neil W. Ashcroft; N. David Mermin (1976). Solid state physics. Saunders College. ISBN   978-0-03-049346-1.
  44. Eckert, Michael (2011). "Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions". Acta Crystallographica A. 68 (1): 30–39. Bibcode:2012AcCrA..68...30E. doi:10.1107/S0108767311039985. PMID   22186281.
  45. Han, Jung Hoon (2010). Solid State Physics (PDF). Sung Kyun Kwan University. Archived from the original (PDF) on 2013-05-20.
  46. 1 2 Perdew, John P.; Ruzsinszky, Adrienn (2010). "Fourteen Easy Lessons in Density Functional Theory" (PDF). International Journal of Quantum Chemistry. 110 (15): 2801–2807. doi:10.1002/qua.22829 . Retrieved 13 May 2012.
  47. Nambu, Yoichiro (8 December 2008). "Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization".
  48. Greiter, Martin (16 March 2005). "Is electromagnetic gauge invariance spontaneously violated in superconductors?". Annals of Physics. 319 (2005): 217–249. arXiv: cond-mat/0503400 . Bibcode:2005AnPhy.319..217G. doi:10.1016/j.aop.2005.03.008.
  49. Leutwyler, H. (1997). "Phonons as Goldstone bosons". Helv. Phys. Acta. 70 (1997): 275–286. arXiv: hep-ph/9609466 .
  50. 1 2 Vojta, Matthias (2003). "Quantum phase transitions". Reports on Progress in Physics. 66 (12): 2069–2110. arXiv: cond-mat/0309604 . Bibcode:2003RPPh...66.2069V. CiteSeerX . doi:10.1088/0034-4885/66/12/R01.
  51. 1 2 3 4 Condensed-Matter Physics, Physics Through the 1990s. National Research Council. 1986. doi:10.17226/626. ISBN   978-0-309-03577-4.
  52. Malcolm F. Collins Professor of Physics McMaster University (1989-03-02). Magnetic Critical Scattering. Oxford University Press, USA. ISBN   978-0-19-536440-8.
  53. Richardson, Robert C. (1988). Experimental methods in Condensed Matter Physics at Low Temperatures. Addison-Wesley. ISBN   978-0-201-15002-5.
  54. 1 2 Chaikin, P. M.; Lubensky, T. C. (1995). Principles of condensed matter physics . Cambridge University Press. ISBN   978-0-521-43224-5.
  55. Wentao Zhang (22 August 2012). Photoemission Spectroscopy on High Temperature Superconductor: A Study of Bi2Sr2CaCu2O8 by Laser-Based Angle-Resolved Photoemission. Springer Science & Business Media. ISBN   978-3-642-32472-7.
  56. Siegel, R. W. (1980). "Positron Annihilation Spectroscopy". Annual Review of Materials Science. 10: 393–425. Bibcode:1980AnRMS..10..393S. doi:10.1146/
  57. Committee on Facilities for Condensed Matter Physics (2004). "Report of the IUPAP working group on Facilities for Condensed Matter Physics : High Magnetic Fields" (PDF). International Union of Pure and Applied Physics. The magnetic field is not simply a spectroscopic tool but is a thermodynamic variable which, along with temperature and pressure, controls the state, the phase transitions and the properties of materials.
  58. 1 2 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 (25 November 2013). High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions. National Academies Press. doi:10.17226/18355. ISBN   978-0-309-28634-3.CS1 maint: multiple names: authors list (link)
  59. Moulton, W. G.; Reyes, A. P. (2006). "Nuclear Magnetic Resonance in Solids at very high magnetic fields". In Herlach, Fritz (ed.). High Magnetic Fields. Science and Technology. World Scientific. ISBN   978-981-277-488-0.
  60. Doiron-Leyraud, Nicolas; et al. (2007). "Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor". Nature. 447 (7144): 565–568. arXiv: 0801.1281 . Bibcode:2007Natur.447..565D. doi:10.1038/nature05872. PMID   17538614.
  61. Buluta, Iulia; Nori, Franco (2009). "Quantum Simulators". Science. 326 (5949): 108–11. Bibcode:2009Sci...326..108B. doi:10.1126/science.1177838. PMID   19797653.
  62. Greiner, Markus; Fölling, Simon (2008). "Condensed-matter physics: Optical lattices". Nature. 453 (7196): 736–738. Bibcode:2008Natur.453..736G. doi:10.1038/453736a. PMID   18528388.
  63. Jaksch, D.; Zoller, P. (2005). "The cold atom Hubbard toolbox". Annals of Physics. 315 (1): 52–79. arXiv: cond-mat/0410614 . Bibcode:2005AnPhy.315...52J. CiteSeerX . doi:10.1016/j.aop.2004.09.010.
  64. Glanz, James (October 10, 2001). "3 Researchers Based in U.S. Win Nobel Prize in Physics". The New York Times. Retrieved 23 May 2012.
  65. Committee on CMMP 2010; Solid State Sciences Committee; Board on Physics and Astronomy; Division on Engineering and Physical Sciences, National Research Council (21 December 2007). Condensed-Matter and Materials Physics: The Science of the World Around Us. National Academies Press. doi:10.17226/11967. ISBN   978-0-309-13409-5.CS1 maint: multiple names: authors list (link)
  66. 1 2 3 Yeh, Nai-Chang (2008). "A Perspective of Frontiers in Modern Condensed Matter Physics" (PDF). AAPPS Bulletin. 18 (2). Retrieved 19 June 2018.

Further reading