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Condensed matter physics

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<div class="hlist"><ul><li><a href="Phase_(matter)" title="Phase (matter)">Phases</a></li><li><a href="Phase_transition" title="Phase transition">Phase transition</a></li><li><a href="Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="State_of_matter" title="State of matter">States of matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Solid" title="Solid">Solid</a></li><li><a href="Liquid" title="Liquid">Liquid</a></li><li><a href="Gas" title="Gas">Gas</a></li><li><a href="Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li><li><a href="Bose_gas" title="Bose gas">Bose gas</a></li><li><a href="Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li><li><a href="Fermi_gas" title="Fermi gas">Fermi gas</a></li><li><a href="Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid</a></li><li><a href="Supersolid" title="Supersolid">Supersolid</a></li><li><a href="Superfluidity" title="Superfluidity">Superfluidity</a></li><li><a href="Luttinger_liquid" title="Luttinger liquid">Luttinger liquid</a></li><li><a href="Time_crystal" title="Time crystal">Time crystal</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Phase phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Order_parameter" class="mw-redirect" title="Order parameter">Order parameter</a></li><li><a href="Phase_transition" title="Phase transition">Phase transition</a></li><li><a href="Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Electronic_band_structure" title="Electronic band structure">Electronic band structure</a></li><li><a href="Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li><li><a href="Mott_insulator" title="Mott insulator">Mott insulator</a></li><li><a href="Semiconductor" title="Semiconductor">Semiconductor</a></li><li><a href="Semimetal" title="Semimetal">Semimetal</a></li><li><a href="Electrical_conductor" title="Electrical conductor">Conductor</a></li><li><a href="Superconductivity" title="Superconductivity">Superconductor</a></li><li><a href="Thermoelectric_effect" title="Thermoelectric effect">Thermoelectric</a></li><li><a href="Piezoelectricity" title="Piezoelectricity">Piezoelectric</a></li><li><a href="Ferroelectricity" title="Ferroelectricity">Ferroelectric</a></li><li><a href="Topological_insulator" title="Topological insulator">Topological insulator</a></li><li><a href="Spin_gapless_semiconductor" title="Spin gapless semiconductor">Spin gapless semiconductor</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></li><li><a href="Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></li><li><a href="Kondo_effect" title="Kondo effect">Kondo effect</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Magnetic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Diamagnetism" title="Diamagnetism">Diamagnet</a></li><li><a href="Superdiamagnetism" title="Superdiamagnetism">Superdiamagnet</a>

<a href="Paramagnetism" title="Paramagnetism">Paramagnet</a></li><li><a href="Superparamagnetism" title="Superparamagnetism">Superparamagnet</a> <a href="Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li><li><a href="Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a> <a href="Metamagnetism" title="Metamagnetism">Metamagnet</a></li><li><a href="Spin_glass" title="Spin glass">Spin glass</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="Quasiparticle" title="Quasiparticle">Quasiparticles</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Phonon" title="Phonon">Phonon</a></li><li><a href="Exciton" title="Exciton">Exciton</a></li><li><a href="Plasmon" title="Plasmon">Plasmon</a> <a href="Polariton" title="Polariton">Polariton</a></li><li><a href="Polaron" title="Polaron">Polaron</a></li><li><a href="Magnon" title="Magnon">Magnon</a></li><li><a href="Roton" title="Roton">Roton</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="Soft_matter" title="Soft matter">Soft matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Amorphous_solid" title="Amorphous solid">Amorphous solid</a></li><li><a href="Colloid" title="Colloid">Colloid</a></li><li><a href="Granular_material" title="Granular material">Granular material</a></li><li><a href="Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li><li><a href="Polymer" title="Polymer">Polymer</a></li></ul></div></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">Van der Waals</a></li><li><a href="Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li><li><a href="Max_von_Laue" title="Max von Laue">von Laue</a></li><li><a href="William_Henry_Bragg" title="William Henry Bragg">Bragg</a></li><li><a href="Peter_Debye" title="Peter Debye">Debye</a></li><li><a href="Felix_Bloch" title="Felix Bloch">Bloch</a></li><li><a href="Lars_Onsager" title="Lars Onsager">Onsager</a></li><li><a href="Neville_Mott" class="mw-redirect" title="Neville Mott">Mott</a></li><li><a href="Rudolf_Peierls" title="Rudolf Peierls">Peierls</a></li><li><a href="Lev_Landau" title="Lev Landau">Landau</a></li><li><a href="Luttinger" class="mw-redirect" title="Luttinger">Luttinger</a></li><li><a href="Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Anderson</a></li><li><a href="John_Hasbrouck_Van_Vleck" title="John Hasbrouck Van Vleck">Van Vleck</a></li><li><a href="John_Hubbard_(physicist)" title="John Hubbard (physicist)">Hubbard</a></li><li><a href="William_Bradford_Shockley" class="mw-redirect" title="William Bradford Shockley">Shockley</a></li><li><a href="John_Bardeen" title="John Bardeen">Bardeen</a></li><li><a href="Leon_Cooper" title="Leon Cooper">Cooper</a></li><li><a href="John_Robert_Schrieffer" title="John Robert Schrieffer">Schrieffer</a></li><li><a href="Brian_Josephson" title="Brian Josephson">Josephson</a></li><li><a href="Louis_N%C3%A9el" title="Louis Néel">Louis Néel</a></li><li><a href="Leo_Esaki" title="Leo Esaki">Esaki</a></li><li><a href="Ivar_Giaever" title="Ivar Giaever">Giaever</a></li><li><a href="Walter_Kohn" title="Walter Kohn">Kohn</a></li><li><a href="Leo_Kadanoff" title="Leo Kadanoff">Kadanoff</a></li><li><a href="Michael_Fisher" title="Michael Fisher">Fisher</a></li><li><a href="Kenneth_G._Wilson" title="Kenneth G. Wilson">Wilson</a></li><li><a href="Klaus_von_Klitzing" title="Klaus von Klitzing">von Klitzing</a></li><li><a href="Gerd_Binnig" title="Gerd Binnig">Binnig</a></li><li><a href="Heinrich_Rohrer" title="Heinrich Rohrer">Rohrer</a></li><li><a href="Johannes_Georg_Bednorz" class="mw-redirect" title="Johannes Georg Bednorz">Bednorz</a></li><li><a href="Karl_Alexander_M%C3%BCller" class="mw-redirect" title="Karl Alexander Müller">Müller</a></li><li><a href="Robert_B._Laughlin" title="Robert B. Laughlin">Laughlin</a></li><li><a href="Horst_Ludwig_St%C3%B6rmer" title="Horst Ludwig Störmer">Störmer</a></li><li><a href="Yang_Chen-Ning" title="Yang Chen-Ning">Yang</a></li><li><a href="Daniel_C._Tsui" title="Daniel C. Tsui">Tsui</a></li><li><a href="Alexei_Alexeyevich_Abrikosov" class="mw-redirect" title="Alexei Alexeyevich Abrikosov">Abrikosov</a></li><li><a href="Vitaly_Lazarevich_Ginzburg" class="mw-redirect" title="Vitaly Lazarevich Ginzburg">Ginzburg</a></li><li><a href="Anthony_James_Leggett" title="Anthony James Leggett">Leggett</a></li><li><a href="Giorgio_Parisi" title="Giorgio Parisi">Parisi</a></li><li><a href="Christof_Wetterich" title="Christof Wetterich">Wetterich</a></li><li><a href="John_Perdew" title="John Perdew">Perdew</a></li></ul></div></div></div></td>

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Condensed matter physics is the field of <a href="Physics" title="Physics">physics</a> that deals with the macroscopic and microscopic physical properties of <a href="Matter" title="Matter">matter</a>, especially the <a href="Solid" title="Solid">solid</a> and <a href="Liquid" title="Liquid">liquid</a> <a href="State_of_matter" title="State of matter">phases</a>, that arise from <a href="Electromagnetic" class="mw-redirect" title="Electromagnetic">electromagnetic</a> forces between <a href="Atom" title="Atom">atoms</a> and <a href="Electrons" class="mw-redirect" title="Electrons">electrons</a>. 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 <a href="Superconductivity" title="Superconductivity">superconducting</a> phase exhibited by certain materials at extremely low <a href="Cryogenic" class="mw-redirect" title="Cryogenic">cryogenic</a> <a href="Temperature" title="Temperature">temperatures</a>, the <a href="Ferromagnet" class="mw-redirect" title="Ferromagnet">ferromagnetic</a> and <a href="Antiferromagnet" class="mw-redirect" title="Antiferromagnet">antiferromagnetic</a> phases of <a href="Spin_(physics)" title="Spin (physics)">spins</a> on <a href="Crystal_lattice" class="mw-redirect" title="Crystal lattice">crystal lattices</a> of atoms, the <a href="Bose%E2%80%93Einstein_condensates" class="mw-redirect" title="Bose–Einstein condensates">Bose–Einstein condensates</a> found in <a href="Ultracold_atom" title="Ultracold atom">ultracold atomic</a> systems, and <a href="Liquid_crystals" class="mw-redirect" title="Liquid crystals">liquid crystals</a>. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the <a href="Physical_law" class="mw-redirect" title="Physical law">physical laws</a> of <a href="Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, <a href="Electromagnetism" title="Electromagnetism">electromagnetism</a>, <a href="Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a>, and other <a href="Theoretical_physics" title="Theoretical physics">physics theories</a> to develop mathematical models and predict the properties of extremely large groups of atoms.<a href="#cite_note-1">[1]</a>

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,<a href="#cite_note-2">[2]</a> and the Division of Condensed Matter Physics is the largest division of the <a href="American_Physical_Society" title="American Physical Society">American Physical Society</a>.<a href="#cite_note-aps-history-3">[3]</a> These include solid state and <a href="Soft_matter" title="Soft matter">soft matter</a> physicists, who study <a href="Quantum_mechanics" title="Quantum mechanics">quantum</a> and non-quantum physical properties of matter respectively.<a href="#cite_note-4">[4]</a> Both types study a great range of materials, providing many research, funding and employment opportunities.<a href="#cite_note-5">[5]</a> The field overlaps with <a href="Chemistry" title="Chemistry">chemistry</a>, <a href="Materials_science" title="Materials science">materials science</a>, <a href="Engineering" title="Engineering">engineering</a> and <a href="Nanotechnology" title="Nanotechnology">nanotechnology</a>, and relates closely to <a href="Atomic_physics" title="Atomic physics">atomic physics</a> and <a href="Biophysics" title="Biophysics">biophysics</a>. The <a href="Theoretical_physics" title="Theoretical physics">theoretical physics</a> of condensed matter shares important concepts and methods with that of <a href="Particle_physics" title="Particle physics">particle physics</a> and <a href="Nuclear_physics" title="Nuclear physics">nuclear physics</a>.<a href="#cite_note-marvincohen2008-6">[6]</a>

A variety of topics in physics such as <a href="Crystallography" title="Crystallography">crystallography</a>, <a href="Metallurgy" title="Metallurgy">metallurgy</a>, <a href="Elasticity_(physics)" title="Elasticity (physics)">elasticity</a>, <a href="Magnetism" title="Magnetism">magnetism</a>, etc., were treated as distinct areas until the 1940s, when they were grouped together as <a href="Solid-state_physics" title="Solid-state physics">solid-state physics</a>. Around the 1960s, the study of physical properties of <a href="Liquid" title="Liquid">liquids</a> was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics.<a href="#cite_note-rmp-7">[7]</a> The <a href="Bell_Labs" title="Bell Labs">Bell Telephone Laboratories</a> was one of the first institutes to conduct a research program in condensed matter physics.<a href="#cite_note-rmp-7">[7]</a> According to the founding director of the <a href="Max_Planck_Institute_for_Solid_State_Research" title="Max Planck Institute for Solid State Research">Max Planck Institute for Solid State Research</a>, physics professor Manuel Cardona, it was <a href="Albert_Einstein" title="Albert Einstein">Albert Einstein</a> who created the modern field of condensed matter physics starting with his seminal 1905 article on the <a href="Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a> and <a href="Photoluminescence" title="Photoluminescence">photoluminescence</a> which opened the fields of <a href="Photoelectron_spectroscopy" class="mw-redirect" title="Photoelectron spectroscopy">photoelectron spectroscopy</a> and <a href="Photoluminescence_spectroscopy" class="mw-redirect" title="Photoluminescence spectroscopy">photoluminescence spectroscopy</a>, and later his 1907 article on the <a href="Specific_heat_of_solids" class="mw-redirect" title="Specific heat of solids">specific heat of solids</a> which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the <a href="Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a>.<a href="#cite_note-Cardona-8">[8]</a> Deputy Director of the Yale Quantum Institute <a href="A._Douglas_Stone" title="A. Douglas Stone">A. Douglas Stone</a> makes a similar priority case for Einstein in his work on the synthetic history of <a href="Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.<a href="#cite_note-Stone-9">[9]</a>

<div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2></div>

According to physicist <a href="Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Philip Warren Anderson</a>, the use of the term "condensed matter" to designate a field of study was coined by him and <a href="Volker_Heine" title="Volker Heine">Volker Heine</a>, when they changed the name of their group at the <a href="Cavendish_Laboratories" class="mw-redirect" title="Cavendish Laboratories">Cavendish Laboratories</a>, <a href="Cambridge" title="Cambridge">Cambridge</a>, from Solid state theory to Theory of Condensed Matter in 1967,<a href="#cite_note-pwa-princeton-10">[10]</a> as they felt it better included their interest in liquids, <a href="Nuclear_matter" title="Nuclear matter">nuclear matter</a>, and so on.<a href="#cite_note-wsn-11">[11]</a><a href="#cite_note-12">[12]</a> Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the <a href="Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer-Verlag</a> journal Physics of Condensed Matter, launched in 1963.<a href="#cite_note-13">[13]</a> 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 <a href="Cold_War" title="Cold War">Cold War</a> politics of the time.<a href="#cite_note-martin-pip-14">[14]</a>

References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids,<a href="#cite_note-Frenkel-15">[15]</a> <a href="Yakov_Frenkel" title="Yakov Frenkel">Yakov Frenkel</a> 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'".

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Timeline_of_condensed_matter_physics" title="Timeline of condensed matter physics">Timeline of condensed matter physics</a></div>

<div class="mw-heading mw-heading3"><h3 id="Classical_physics">Classical physics</h3></div>

One of the first studies of condensed states of matter was by <a href="People_of_England" class="mw-redirect" title="People of England">English</a> <a href="Chemist" title="Chemist">chemist</a> <a href="Humphry_Davy" title="Humphry Davy">Humphry Davy</a>, in the first decades of the nineteenth century. Davy observed that of the forty <a href="Chemical_element" title="Chemical element">chemical elements</a> known at the time, twenty-six had <a href="Metal" title="Metal">metallic</a> properties such as <a href="Lustre_(mineralogy)" title="Lustre (mineralogy)">lustre</a>, <a href="Ductility" title="Ductility">ductility</a> and high electrical and thermal conductivity.<a href="#cite_note-goodstein-16">[16]</a> This indicated that the atoms in <a href="John_Dalton" title="John Dalton">John Dalton</a>'s <a href="Atomic_theory" class="mw-redirect" title="Atomic theory">atomic theory</a> were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as <a href="Nitrogen" title="Nitrogen">nitrogen</a> and <a href="Hydrogen" title="Hydrogen">hydrogen</a> could be liquefied under the right conditions and would then behave as metals.<a href="#cite_note-davy-1839-17">[17]</a><a href="#cite_note-19">[note 1]</a>

In 1823, <a href="Michael_Faraday" title="Michael Faraday">Michael Faraday</a>, then an assistant in Davy's lab, successfully liquefied <a href="Chlorine" title="Chlorine">chlorine</a> and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and <a href="Oxygen" title="Oxygen">oxygen</a>.<a href="#cite_note-goodstein-16">[16]</a> Shortly after, in 1869, <a href="People_of_Ireland" class="mw-redirect" title="People of Ireland">Irish</a> chemist <a href="Thomas_Andrews_(scientist)" title="Thomas Andrews (scientist)">Thomas Andrews</a> studied the <a href="Phase_transition" title="Phase transition">phase transition</a> from a liquid to a gas and coined the term <a href="Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">critical point</a> to describe the condition where a gas and a liquid were indistinguishable as phases,<a href="#cite_note-thomasandrews-20">[19]</a> and <a href="Netherlands" title="Netherlands">Dutch</a> physicist <a href="Johannes_van_der_Waals" class="mw-redirect" title="Johannes van der Waals">Johannes van der Waals</a> supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.<a href="#cite_note-atkins-21">[20]</a>: 35–38 By 1908, <a href="James_Dewar" title="James Dewar">James Dewar</a> and <a href="Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Heike Kamerlingh Onnes</a> were successfully able to liquefy hydrogen and the then newly discovered <a href="Helium" title="Helium">helium</a> respectively.<a href="#cite_note-goodstein-16">[16]</a>

<a href="Paul_Drude" title="Paul Drude">Paul Drude</a> in 1900 proposed the first theoretical model for a classical <a href="Electron" title="Electron">electron</a> moving through a metallic solid.<a href="#cite_note-marvincohen2008-6">[6]</a> 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 <a href="Wiedemann%E2%80%93Franz_law" title="Wiedemann–Franz law">Wiedemann–Franz law</a>.<a href="#cite_note-Kittel_1996-22">[21]</a><a href="#cite_note-Hoddeson-1992-23">[22]</a>: 27–29 However, despite the success of <a href="Drude_model" title="Drude model">Drude's model</a>, it had one notable problem: it was unable to correctly explain the electronic contribution to the <a href="Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.<a href="#cite_note-Kragh2002-24">[23]</a>: 366–368

In 1911, three years after helium was first liquefied, Onnes working at <a href="University_of_Leiden" class="mw-redirect" title="University of Leiden">University of Leiden</a> discovered <a href="Superconductivity" title="Superconductivity">superconductivity</a> in <a href="Mercury_(element)" title="Mercury (element)">mercury</a>, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.<a href="#cite_note-vanDelft2010-25">[24]</a> The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.<a href="#cite_note-Slichter-AIP-supercond-26">[25]</a> <a href="Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, 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."<a href="#cite_note-Schmalian-2010-27">[26]</a>

<div class="mw-heading mw-heading3"><h3 id="Advent_of_quantum_mechanics">Advent of quantum mechanics</h3></div>

Drude's classical model was augmented by <a href="Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>, <a href="Arnold_Sommerfeld" title="Arnold Sommerfeld">Arnold Sommerfeld</a>, <a href="Felix_Bloch" title="Felix Bloch">Felix Bloch</a> and other physicists. Pauli realized that the free electrons in metal must obey the <a href="Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a>. Using this idea, he developed the theory of <a href="Paramagnetism" title="Paramagnetism">paramagnetism</a> in 1926. Shortly after, Sommerfeld incorporated the <a href="Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a> into the <a href="Free_electron_model" title="Free electron model">free electron model</a> and made it better to explain the heat capacity. Two years later, Bloch used <a href="Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> to describe the motion of an electron in a periodic lattice.<a href="#cite_note-Kragh2002-24">[23]</a>: 366–368

The mathematics of crystal structures developed by <a href="Auguste_Bravais" title="Auguste Bravais">Auguste Bravais</a>, <a href="Yevgraf_Fyodorov" class="mw-redirect" title="Yevgraf Fyodorov">Yevgraf Fyodorov</a> and others was used to classify crystals by their <a href="Symmetry_group" title="Symmetry group">symmetry group</a>, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935.<a href="#cite_note-Aroyo-2006-28">[27]</a> <a href="Band_theory" class="mw-redirect" title="Band theory">Band structure calculations</a> were first used in 1930 to predict the properties of new materials, and in 1947 <a href="John_Bardeen" title="John Bardeen">John Bardeen</a>, <a href="Walter_Brattain" title="Walter Brattain">Walter Brattain</a> and <a href="William_Shockley" title="William Shockley">William Shockley</a> developed the first <a href="Semiconductor" title="Semiconductor">semiconductor</a>-based <a href="Transistor" title="Transistor">transistor</a>, heralding a revolution in electronics.<a href="#cite_note-marvincohen2008-6">[6]</a>

In 1879, <a href="Edwin_Herbert_Hall" class="mw-redirect" title="Edwin Herbert Hall">Edwin Herbert Hall</a> working at the <a href="Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a> 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.<a href="#cite_note-29">[28]</a> This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the <a href="Hall_effect" title="Hall effect">Hall effect</a>, 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, <a href="Lev_Landau" title="Lev Landau">Lev Landau</a> in 1930 developed the theory of <a href="Landau_quantization" class="mw-redirect" title="Landau quantization">Landau quantization</a> and laid the foundation for a theoretical explanation of the <a href="Quantum_Hall_effect" title="Quantum Hall effect">quantum Hall effect</a> which was discovered half a century later.<a href="#cite_note-30">[29]</a>: 458–460 <a href="#cite_note-31">[30]</a>

Magnetism as a property of matter has been known in China since 4000 BC.<a href="#cite_note-mattis-magnetism-2006-32">[31]</a>: 1–2 However, the first modern studies of magnetism only started with the development of <a href="Electrodynamics" class="mw-redirect" title="Electrodynamics">electrodynamics</a> by Faraday, <a href="James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a> and others in the nineteenth century, which included classifying materials as <a href="Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a>, <a href="Paramagnetic" class="mw-redirect" title="Paramagnetic">paramagnetic</a> and <a href="Diamagnetic" class="mw-redirect" title="Diamagnetic">diamagnetic</a> based on their response to magnetization.<a href="#cite_note-Chatterjee-2004-ferromagnetism-33">[32]</a> <a href="Pierre_Curie" title="Pierre Curie">Pierre Curie</a> studied the dependence of magnetization on temperature and discovered the <a href="Curie_point" class="mw-redirect" title="Curie point">Curie point</a> phase transition in ferromagnetic materials.<a href="#cite_note-mattis-magnetism-2006-32">[31]</a> In 1906, <a href="Pierre_Weiss" title="Pierre Weiss">Pierre Weiss</a> introduced the concept of <a href="Magnetic_domain" title="Magnetic domain">magnetic domains</a> to explain the main properties of ferromagnets.<a href="#cite_note-Visintin-domains-34">[33]</a>: 9 The first attempt at a microscopic description of magnetism was by <a href="Wilhelm_Lenz" title="Wilhelm Lenz">Wilhelm Lenz</a> and <a href="Ernst_Ising" title="Ernst Ising">Ernst Ising</a> through the <a href="Ising_model" title="Ising model">Ising model</a> that described magnetic materials as consisting of a periodic lattice of <a href="Spin_(physics)" title="Spin (physics)">spins</a> that collectively acquired magnetization.<a href="#cite_note-mattis-magnetism-2006-32">[31]</a> The Ising model was solved exactly to show that <a href="Spontaneous_magnetization" title="Spontaneous magnetization">spontaneous magnetization</a> can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on <a href="Spin_wave" title="Spin wave">spin waves</a> and <a href="N%C3%A9el" class="mw-redirect" title="Néel">Néel</a> on <a href="Antiferromagnetism" title="Antiferromagnetism">antiferromagnetism</a> led to developing new magnetic materials with applications to <a href="Magnetic_storage" title="Magnetic storage">magnetic storage</a> devices.<a href="#cite_note-mattis-magnetism-2006-32">[31]</a>: 36–38, g48

<div class="mw-heading mw-heading3"><h3 id="Modern_many-body_physics">Modern many-body physics</h3></div>

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 <a href="Superconductivity" title="Superconductivity">superconductivity</a> and the <a href="Kondo_effect" title="Kondo effect">Kondo effect</a>.<a href="#cite_note-Coleman-2003-36">[35]</a> After <a href="World_War_II" title="World War II">World War II</a>, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of <a href="Collective_excitation" class="mw-redirect" title="Collective excitation">collective excitation</a> modes of solids and the important notion of a quasiparticle. Soviet physicist <a href="Lev_Landau" title="Lev Landau">Lev Landau</a> used the idea for the <a href="Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid theory</a> wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.<a href="#cite_note-Coleman-2003-36">[35]</a> Landau also developed a <a href="Mean-field_theory" title="Mean-field theory">mean-field theory</a> for continuous phase transitions, which described ordered phases as <a href="Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">spontaneous breakdown of symmetry</a>. The theory also introduced the notion of an <a href="Order_parameter" class="mw-redirect" title="Order parameter">order parameter</a> to distinguish between ordered phases.<a href="#cite_note-Kadanoff-2009-37">[36]</a> Eventually in 1956, <a href="John_Bardeen" title="John Bardeen">John Bardeen</a>, <a href="Leon_Cooper" title="Leon Cooper">Leon Cooper</a> and <a href="Robert_Schrieffer" class="mw-redirect" title="Robert Schrieffer">Robert Schrieffer</a> developed the so-called <a href="BCS_theory" title="BCS theory">BCS theory</a> of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by <a href="Phonon" title="Phonon">phonons</a> in the lattice can give rise to a bound state called a <a href="Cooper_pair" title="Cooper pair">Cooper pair</a>.<a href="#cite_note-coleman-38">[37]</a>

The study of phase transitions and the critical behavior of observables, termed <a href="Critical_phenomena" title="Critical phenomena">critical phenomena</a>, was a major field of interest in the 1960s.<a href="#cite_note-Fisher-rmp-1998-40">[39]</a> <a href="Leo_Kadanoff" title="Leo Kadanoff">Leo Kadanoff</a>, <a href="Benjamin_Widom" title="Benjamin Widom">Benjamin Widom</a> and <a href="Michael_Fisher" title="Michael Fisher">Michael Fisher</a> developed the ideas of <a href="Critical_exponent" title="Critical exponent">critical exponents</a> and <a href="Widom_scaling" title="Widom scaling">widom scaling</a>. These ideas were unified by <a href="Kenneth_G._Wilson" title="Kenneth G. Wilson">Kenneth G. Wilson</a> in 1972, under the formalism of the <a href="Renormalization_group" title="Renormalization group">renormalization group</a> in the context of quantum field theory.<a href="#cite_note-Fisher-rmp-1998-40">[39]</a>

The <a href="Quantum_Hall_effect" title="Quantum Hall effect">quantum Hall effect</a> was discovered by <a href="Klaus_von_Klitzing" title="Klaus von Klitzing">Klaus von Klitzing</a>, Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{2}/h}">

<msup>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle e^{2}/h}</annotation>

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</math><img src="./6224e6d40f7748ccebba5199a177b7d978dc93e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.639ex; height:3.176ex;" alt="{\displaystyle e^{2}/h}" loading="lazy">.(see figure) The effect was observed to be independent of parameters such as system size and impurities.<a href="#cite_note-von_Klitzing-39">[38]</a> In 1981, theorist <a href="Robert_Laughlin" class="mw-redirect" title="Robert Laughlin">Robert Laughlin</a> 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 <a href="Chern_class#Chern_numbers" title="Chern class">Chern number</a>, whose relevance for the band structure of solids was formulated by <a href="David_J._Thouless" class="mw-redirect" title="David J. Thouless">David J. Thouless</a> and collaborators.<a href="#cite_note-Avron-hall-2003-41">[40]</a><a href="#cite_note-Thouless1998-42">[41]</a>: 69, 74 Shortly after, in 1982, <a href="Horst_St%C3%B6rmer" class="mw-redirect" title="Horst Störmer">Horst Störmer</a> and <a href="Daniel_Tsui" class="mw-redirect" title="Daniel Tsui">Daniel Tsui</a> observed the <a href="Fractional_quantum_Hall_effect" title="Fractional quantum Hall effect">fractional quantum Hall effect</a> where the conductance was now a rational multiple of the constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{2}/h}">

<msup>

</mrow>

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<annotation encoding="application/x-tex">{\displaystyle e^{2}/h}</annotation>

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</math><img src="./6224e6d40f7748ccebba5199a177b7d978dc93e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.639ex; height:3.176ex;" alt="{\displaystyle e^{2}/h}" loading="lazy">. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a <a href="Variational_method" class="mw-redirect" title="Variational method">variational method</a> solution, named the <a href="Laughlin_wavefunction" title="Laughlin wavefunction">Laughlin wavefunction</a>.<a href="#cite_note-wen-1992-43">[42]</a> The study of topological properties of the fractional Hall effect remains an active field of research.<a href="#cite_note-:0-44">[43]</a> Decades later, the aforementioned topological band theory advanced by <a href="David_J._Thouless" class="mw-redirect" title="David J. Thouless">David J. Thouless</a> and collaborators<a href="#cite_note-45">[44]</a> was further expanded leading to the discovery of <a href="Topological_insulator" title="Topological insulator">topological insulators</a>.<a href="#cite_note-46">[45]</a><a href="#cite_note-47">[46]</a>

In 1986, <a href="Karl_Alexander_M%C3%BCller" class="mw-redirect" title="Karl Alexander Müller">Karl Müller</a> and <a href="Johannes_Bednorz" class="mw-redirect" title="Johannes Bednorz">Johannes Bednorz</a> discovered the first <a href="High_temperature_superconductor" class="mw-redirect" title="High temperature superconductor">high temperature superconductor</a>, La2-xBaxCuO4, which is superconducting at temperatures as high as 39 <a href="Kelvin" title="Kelvin">kelvin</a>.<a href="#cite_note-48">[47]</a> It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.<a href="#cite_note-physics-world_str-el-49">[48]</a> A satisfactory theoretical description of high-temperature superconductors is still not known and the field of <a href="Strongly_correlated_material" title="Strongly correlated material">strongly correlated materials</a> continues to be an active research topic.

In 2012, several groups released preprints which suggest that <a href="Samarium#Samarium_hexaboride" title="Samarium">samarium hexaboride</a> has the properties of a <a href="Topological_insulator" title="Topological insulator">topological insulator</a><a href="#cite_note-Nature-1-50">[49]</a> in accord with the earlier theoretical predictions.<a href="#cite_note-TKI-51">[50]</a> Since samarium hexaboride is an established <a href="Kondo_insulator" title="Kondo insulator">Kondo insulator</a>, 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.

<div class="mw-heading mw-heading2"><h2 id="Theoretical">Theoretical</h2></div>

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 <a href="Drude_model" title="Drude model">Drude model</a>, the <a href="Electronic_band_structure" title="Electronic band structure">band structure</a> and the <a href="Density_functional_theory" title="Density functional theory">density functional theory</a>. Theoretical models have also been developed to study the physics of <a href="Phase_transition" title="Phase transition">phase transitions</a>, such as the <a href="Ginzburg%E2%80%93Landau_theory" title="Ginzburg–Landau theory">Ginzburg–Landau theory</a>, <a href="Critical_exponent" title="Critical exponent">critical exponents</a> and the use of mathematical methods of <a href="Quantum_field_theory" title="Quantum field theory">quantum field theory</a> and the <a href="Renormalization_group" title="Renormalization group">renormalization group</a>. Modern theoretical studies involve the use of <a href="Numerical_computation" class="mw-redirect" title="Numerical computation">numerical computation</a> of electronic structure and mathematical tools to understand phenomena such as <a href="High-temperature_superconductivity" title="High-temperature superconductivity">high-temperature superconductivity</a>, <a href="Topological_phase" class="mw-redirect" title="Topological phase">topological phases</a>, and <a href="Gauge_symmetry" class="mw-redirect" title="Gauge symmetry">gauge symmetries</a>.

<div class="mw-heading mw-heading3"><h3 id="Emergence">Emergence</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Emergence" title="Emergence">Emergence</a></div>

Theoretical understanding of condensed matter physics is closely related to the notion of <a href="Emergence" title="Emergence">emergence</a>, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents.<a href="#cite_note-coleman-38">[37]</a><a href="#cite_note-:0-44">[43]</a> 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.<a href="#cite_note-nsf-emergence-52">[51]</a> Similarly, models of condensed matter systems have been studied where <a href="Collective_excitation" class="mw-redirect" title="Collective excitation">collective excitations</a> behave like <a href="Photon" title="Photon">photons</a> and <a href="Electron" title="Electron">electrons</a>, thereby describing <a href="Electromagnetism" title="Electromagnetism">electromagnetism</a> as an emergent phenomenon.<a href="#cite_note-levin-rmp-53">[52]</a> Emergent properties can also occur at the interface between materials: one example is the <a href="Lanthanum_aluminate-strontium_titanate_interface" title="Lanthanum aluminate-strontium titanate interface">lanthanum aluminate-strontium titanate interface</a>, where two band-insulators are joined to create conductivity and <a href="Superconductivity" title="Superconductivity">superconductivity</a>.

<div class="mw-heading mw-heading3"><h3 id="Electronic_theory_of_solids">Electronic theory of solids</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electronic_band_structure" title="Electronic band structure">Electronic band structure</a></div>

The metallic state has historically been an important building block for studying properties of solids.<a href="#cite_note-AshcroftMermin1976-54">[53]</a> The first theoretical description of metals was given by <a href="Paul_Drude" title="Paul Drude">Paul Drude</a> in 1900 with the <a href="Drude_model" title="Drude model">Drude model</a>, which explained electrical and thermal properties by describing a metal as an <a href="Ideal_gas" title="Ideal gas">ideal gas</a> of then-newly discovered <a href="Electron" title="Electron">electrons</a>. He was able to derive the empirical <a href="Wiedemann-Franz_law" class="mw-redirect" title="Wiedemann-Franz law">Wiedemann-Franz law</a> and get results in close agreement with the experiments.<a href="#cite_note-Hoddeson-1992-23">[22]</a>: 90–91 This classical model was then improved by <a href="Arnold_Sommerfeld" title="Arnold Sommerfeld">Arnold Sommerfeld</a> who incorporated the <a href="Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a> of electrons and was able to explain the anomalous behavior of the <a href="Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> of metals in the <a href="Wiedemann%E2%80%93Franz_law" title="Wiedemann–Franz law">Wiedemann–Franz law</a>.<a href="#cite_note-Hoddeson-1992-23">[22]</a>: 101–103 In 1912, The structure of crystalline solids was studied by <a href="Max_von_Laue" title="Max von Laue">Max von Laue</a> and Paul Knipping, when they observed the <a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a> pattern of crystals, and concluded that crystals get their structure from periodic <a href="Lattice_model_(physics)" title="Lattice model (physics)">lattices</a> of atoms.<a href="#cite_note-Hoddeson-1992-23">[22]</a>: 48 <a href="#cite_note-55">[54]</a> In 1928, Swiss physicist <a href="Felix_Bloch" title="Felix Bloch">Felix Bloch</a> provided a wave function solution to the <a href="Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> with a <a href="Periodic_function" title="Periodic function">periodic</a> potential, known as <a href="Bloch's_theorem" title="Bloch's theorem">Bloch's theorem</a>.<a href="#cite_note-han-2010-56">[55]</a>

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.<a href="#cite_note-perdew-2010-57">[56]</a> The <a href="Thomas%E2%80%93Fermi_model" title="Thomas–Fermi model">Thomas–Fermi theory</a>, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a <a href="Variational_method" class="mw-redirect" title="Variational method">variational parameter</a>. Later in the 1930s, <a href="Douglas_Hartree" title="Douglas Hartree">Douglas Hartree</a>, <a href="Vladimir_Fock" title="Vladimir Fock">Vladimir Fock</a> and <a href="John_C._Slater" title="John C. Slater">John Slater</a> developed the so-called <a href="Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock wavefunction</a> as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for <a href="Exchange_symmetry" class="mw-redirect" title="Exchange symmetry">exchange statistics</a> 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.<a href="#cite_note-AshcroftMermin1976-54">[53]</a>: 330–337 Finally in 1964–65, <a href="Walter_Kohn" title="Walter Kohn">Walter Kohn</a>, <a href="Pierre_Hohenberg" title="Pierre Hohenberg">Pierre Hohenberg</a> and <a href="Lu_Jeu_Sham" title="Lu Jeu Sham">Lu Jeu Sham</a> proposed the <a href="Density_functional_theory" title="Density functional theory">density functional theory</a> (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.<a href="#cite_note-perdew-2010-57">[56]</a>

<div class="mw-heading mw-heading3"><h3 id="Symmetry_breaking">Symmetry breaking</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Symmetry_breaking" title="Symmetry breaking">Symmetry breaking</a></div>

Some states of matter exhibit symmetry breaking, where the relevant laws of physics possess some form of <a href="Symmetry_(physics)" title="Symmetry (physics)">symmetry</a> that is broken. A common example is <a href="Crystal" title="Crystal">crystalline solids</a>, which break continuous <a href="Translational_symmetry" title="Translational symmetry">translational symmetry</a>. Other examples include magnetized <a href="Ferromagnetism" title="Ferromagnetism">ferromagnets</a>, which break <a href="Rotational_symmetry" title="Rotational symmetry">rotational symmetry</a>, and more exotic states such as the ground state of a <a href="BCS_theory" title="BCS theory">BCS</a> <a href="Superconductor" class="mw-redirect" title="Superconductor">superconductor</a>, that breaks <a href="U(1)" class="mw-redirect" title="U(1)">U(1)</a> phase rotational symmetry.<a href="#cite_note-58">[57]</a><a href="#cite_note-59">[58]</a>

<a href="Goldstone's_theorem" class="mw-redirect" title="Goldstone's theorem">Goldstone's theorem</a> in <a href="Quantum_field_theory" title="Quantum field theory">quantum field theory</a> states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone <a href="Boson" title="Boson">bosons</a>. For example, in crystalline solids, these correspond to <a href="Phonon" title="Phonon">phonons</a>, which are quantized versions of lattice vibrations.<a href="#cite_note-goldstone-60">[59]</a>

<div class="mw-heading mw-heading3"><h3 id="Phase_transition">Phase transition</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Phase_transition" title="Phase transition">Phase transition</a></div>

Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as <a href="Temperature" title="Temperature">temperature</a>, <a href="Pressure" title="Pressure">pressure</a>, 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 <a href="Quantum_phase_transition" title="Quantum phase transition">quantum phase transitions</a>, the temperature is set to <a href="Absolute_zero" title="Absolute zero">absolute zero</a>, and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed by <a href="Quantum_fluctuation" title="Quantum fluctuation">quantum fluctuations</a> originating from the <a href="Heisenberg_uncertainty_principle" class="mw-redirect" title="Heisenberg uncertainty principle">Heisenberg uncertainty principle</a>. Here, the different quantum phases of the system refer to distinct <a href="Ground_state" title="Ground state">ground states</a> of the <a href="Hamiltonian_matrix" title="Hamiltonian matrix">Hamiltonian matrix</a>. 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.<a href="#cite_note-Vojta2003-61">[60]</a>

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 <a href="Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">critical point</a>. Near the critical point, systems undergo critical behavior, wherein several of their properties such as <a href="Correlation_length" class="mw-redirect" title="Correlation length">correlation length</a>, <a href="Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a>, and <a href="Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a> diverge exponentially.<a href="#cite_note-Vojta2003-61">[60]</a> These critical phenomena present serious challenges to physicists because normal <a href="Macroscopic_scale" title="Macroscopic scale">macroscopic</a> 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.<a href="#cite_note-NRC1986-62">[61]</a>: 75ff

The simplest theory that can describe continuous phase transitions is the <a href="Ginzburg%E2%80%93Landau_theory" title="Ginzburg–Landau theory">Ginzburg–Landau theory</a>, which works in the so-called <a href="Mean-field_approximation" class="mw-redirect" title="Mean-field approximation">mean-field approximation</a>. 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.<a href="#cite_note-University1989-63">[62]</a>: 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. <a href="Renormalization_group" title="Renormalization group">Renormalization group</a> 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.<a href="#cite_note-NRC1986-62">[61]</a>: 11

<div class="mw-heading mw-heading2"><h2 id="Experimental">Experimental</h2></div>

Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of <a href="Electric_field" title="Electric field">electric</a> and <a href="Magnetic_field" title="Magnetic field">magnetic fields</a>, measuring <a href="Response_function" class="mw-redirect" title="Response function">response functions</a>, <a href="Transport_theory_(statistical_physics)" class="mw-redirect" title="Transport theory (statistical physics)">transport properties</a> and <a href="Thermometry" class="mw-redirect" title="Thermometry">thermometry</a>.<a href="#cite_note-exptcm-64">[63]</a> Commonly used experimental methods include <a href="Spectroscopy" title="Spectroscopy">spectroscopy</a>, with probes such as <a href="X-ray_spectroscopy" title="X-ray spectroscopy">X-rays</a>, <a href="Infrared_spectroscopy" title="Infrared spectroscopy">infrared light</a> and <a href="Inelastic_neutron_scattering" class="mw-redirect" title="Inelastic neutron scattering">inelastic neutron scattering</a>; study of thermal response, such as <a href="Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> and measuring transport via thermal and heat <a href="Conduction_(heat)" class="mw-redirect" title="Conduction (heat)">conduction</a>.

<div class="mw-heading mw-heading3"><h3 id="Scattering">Scattering</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Scattering" title="Scattering">Scattering</a></div>

Several condensed matter experiments involve scattering of an experimental probe, such as <a href="X-ray" title="X-ray">X-ray</a>, optical <a href="Photon" title="Photon">photons</a>, <a href="Neutron" title="Neutron">neutrons</a>, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest. <a href="Visible_light" class="mw-redirect" title="Visible light">Visible light</a> has energy on the scale of 1 <a href="Electron_volt" class="mw-redirect" title="Electron volt">electron volt</a> (eV) and is used as a scattering probe to measure variations in material properties such as the <a href="Dielectric_constant" class="mw-redirect" title="Dielectric constant">dielectric constant</a> and <a href="Refractive_index" title="Refractive index">refractive index</a>. X-rays have energies of the order of 10 <a href="Electron_volt" class="mw-redirect" title="Electron volt">keV</a> and hence are able to probe atomic length scales, and are used to measure variations in electron charge density and crystal structure.<a href="#cite_note-chaikin-lubensky-65">[64]</a>: 33–34

<a href="Neutron" title="Neutron">Neutrons</a> can also probe atomic length scales and are used to study the scattering off nuclei and electron <a href="Spin_(physics)" title="Spin (physics)">spins</a> and magnetization (as neutrons have spin but no charge). Coulomb and <a href="Mott_scattering" title="Mott scattering">Mott scattering</a> measurements can be made by using <a href="Electron_beams" class="mw-redirect" title="Electron beams">electron beams</a> as scattering probes.<a href="#cite_note-chaikin-lubensky-65">[64]</a>: 33–34 <a href="#cite_note-Zhang2012-66">[65]</a>: 39–43 Similarly, <a href="Positron" title="Positron">positron</a> annihilation can be used as an indirect measurement of local electron density.<a href="#cite_note-siegel-1980-67">[66]</a> <a href="Laser_spectroscopy" class="mw-redirect" title="Laser spectroscopy">Laser spectroscopy</a> is an excellent tool for studying the microscopic properties of a medium, for example, to study <a href="Forbidden_transition" class="mw-redirect" title="Forbidden transition">forbidden transitions</a> in media with <a href="Non-linear_optics" class="mw-redirect" title="Non-linear optics">nonlinear optical spectroscopy</a>.<a href="#cite_note-NRC1986-62">[61]</a> : 258–259

<div class="mw-heading mw-heading3"><h3 id="External_magnetic_fields">External magnetic fields</h3></div>

In experimental condensed matter physics, external <a href="Magnetic_field" title="Magnetic field">magnetic fields</a> act as <a href="Thermodynamic_variable" class="mw-redirect" title="Thermodynamic variable">thermodynamic variables</a> that control the state, phase transitions and properties of material systems.<a href="#cite_note-iupap-report-68">[67]</a> <a href="Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">Nuclear magnetic resonance</a> (NMR) is a method by which external <a href="Magnetic_fields" class="mw-redirect" title="Magnetic fields">magnetic fields</a> 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 <a href="Tesla_(unit)" title="Tesla (unit)">tesla</a>. Higher magnetic fields can improve the quality of NMR measurement data.<a href="#cite_note-StatesAstronomy2013-69">[68]</a>: 69 <a href="#cite_note-70">[69]</a>: 185 <a href="Quantum_oscillations" title="Quantum oscillations">Quantum oscillations</a> is another experimental method where high magnetic fields are used to study material properties such as the geometry of the <a href="Fermi_surface" title="Fermi surface">Fermi surface</a>.<a href="#cite_note-doiron-leyraud2007-71">[70]</a> High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized <a href="Magnetoelectric_effect" title="Magnetoelectric effect">magnetoelectric effect</a>, image <a href="Magnetic_monopole" title="Magnetic monopole">magnetic monopole</a>, and the half-integer <a href="Quantum_Hall_effect" title="Quantum Hall effect">quantum Hall effect</a>.<a href="#cite_note-StatesAstronomy2013-69">[68]</a>: 57

<div class="mw-heading mw-heading3"><h3 id="Magnetic_resonance_spectroscopy">Magnetic resonance spectroscopy</h3></div>

The <a href="Local_structure" title="Local structure">local structure</a>, as well as the structure of the nearest neighbour atoms, can be investigated in condensed matter with magnetic resonance methods, such as <a href="Electron_paramagnetic_resonance" title="Electron paramagnetic resonance">electron paramagnetic resonance</a> (EPR) and <a href="Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">nuclear magnetic resonance</a> (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 <a href="Atomic_nucleus" title="Atomic nucleus">nuclei</a> become the probe of these <a href="Hyperfine_structure" title="Hyperfine structure">hyperfine interactions</a>), 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 <a href="Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">NMR</a>, <a href="Nuclear_quadrupole_resonance" title="Nuclear quadrupole resonance">nuclear quadrupole resonance</a> (NQR), implanted radioactive probes as in the case of <a href="Muon_spin_spectroscopy" title="Muon spin spectroscopy">muon spin spectroscopy</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle \mu }</annotation>

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</math><img src="./9fd47b2a39f7a7856952afec1f1db72c67af6161.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }" loading="lazy">SR), <a href="M%C3%B6ssbauer_spectroscopy" title="Mössbauer spectroscopy">Mössbauer spectroscopy</a>, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">

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<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>

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</math><img src="./7ed48a5e36207156fb792fa79d29925d2f7901e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" loading="lazy">NMR and <a href="Perturbed_angular_correlation" title="Perturbed angular correlation">perturbed angular correlation</a> (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.

<div class="mw-heading mw-heading3"><h3 id="Cold_atomic_gases">Cold atomic gases</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Optical_lattice" title="Optical lattice">Optical lattice</a></div>

<a href="Ultracold_atom" title="Ultracold atom">Ultracold atom</a> trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in <a href="Atomic%2C_molecular%2C_and_optical_physics" title="Atomic, molecular, and optical physics">atomic, molecular, and optical physics</a>. The method involves using optical lasers to form an <a href="Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference pattern</a>, 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 <a href="Geometrical_frustration" title="Geometrical frustration">frustrated magnets</a>.<a href="#cite_note-buluta-science2009-72">[71]</a> In particular, they are used to engineer one-, two- and three-dimensional lattices for a <a href="Hubbard_model" title="Hubbard model">Hubbard model</a> with pre-specified parameters, and to study phase transitions for <a href="Antiferromagnetism" title="Antiferromagnetism">antiferromagnetic</a> and <a href="Spin_liquid" class="mw-redirect" title="Spin liquid">spin liquid</a> ordering.<a href="#cite_note-greiner-nature2008-73">[72]</a><a href="#cite_note-jaksch-aop2005-74">[73]</a><a href="#cite_note-:0-44">[43]</a>

In 1995, a gas of <a href="Rubidium" title="Rubidium">rubidium</a> atoms cooled down to a temperature of 170 <a href="Kelvin" title="Kelvin">nK</a> was used to experimentally realize the <a href="Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a>, a novel state of matter originally predicted by <a href="S._N._Bose" class="mw-redirect" title="S. N. Bose">S. N. Bose</a> and <a href="Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, wherein a large number of atoms occupy one <a href="Quantum_state" title="Quantum state">quantum state</a>.<a href="#cite_note-nytimes-BEC-75">[74]</a>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

Research in condensed matter physics<a href="#cite_note-:0-44">[43]</a><a href="#cite_note-76">[75]</a> has given rise to several device applications, such as the development of the <a href="Semiconductor" title="Semiconductor">semiconductor</a> <a href="Transistor" title="Transistor">transistor</a>,<a href="#cite_note-marvincohen2008-6">[6]</a> <a href="Laser" title="Laser">laser</a> technology,<a href="#cite_note-NRC1986-62">[61]</a> <a href="Magnetic_storage" title="Magnetic storage">magnetic storage</a>, <a href="Liquid_crystals" class="mw-redirect" title="Liquid crystals">liquid crystals</a>, <a href="Optical_fibres" class="mw-redirect" title="Optical fibres">optical fibres</a><a href="#cite_note-77">[76]</a> and several phenomena studied in the context of <a href="Nanotechnology" title="Nanotechnology">nanotechnology</a>.<a href="#cite_note-2010Committee2007-78">[77]</a>: 111ff Methods such as <a href="Scanning_tunneling_microscope" title="Scanning tunneling microscope">scanning-tunneling microscopy</a> can be used to control processes at the <a href="Nanometer" class="mw-redirect" title="Nanometer">nanometer</a> scale, and have given rise to the study of nanofabrication.<a href="#cite_note-yeh-perspective-79">[78]</a> Such molecular machines were developed for example by Nobel laureates in chemistry <a href="Ben_Feringa" title="Ben Feringa">Ben Feringa</a>, <a href="Jean-Pierre_Sauvage" title="Jean-Pierre Sauvage">Jean-Pierre Sauvage</a> and <a href="Fraser_Stoddart" title="Fraser Stoddart">Fraser Stoddart</a>. Feringa and his team developed multiple molecular machines such as the <a href="Molecular_car" class="mw-redirect" title="Molecular car">molecular car</a>, molecular windmill and many more.<a href="#cite_note-80">[79]</a>

In <a href="Quantum_computation" class="mw-redirect" title="Quantum computation">quantum computation</a>, information is represented by quantum bits, or <a href="Qubit" title="Qubit">qubits</a>. The qubits may <a href="Quantum_decoherence" title="Quantum decoherence">decohere</a> 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 <a href="Josephson_junction" class="mw-redirect" title="Josephson junction">Josephson junction</a> qubits, <a href="Spintronic" class="mw-redirect" title="Spintronic">spintronic</a> qubits using the <a href="Spin_(physics)" title="Spin (physics)">spin</a> orientation of magnetic materials, and the topological non-Abelian <a href="Anyon" title="Anyon">anyons</a> from <a href="Fractional_quantum_Hall_effect" title="Fractional quantum Hall effect">fractional quantum Hall effect</a> states.<a href="#cite_note-yeh-perspective-79">[78]</a>

Condensed matter physics also has important uses for <a href="Biomedicine" title="Biomedicine">biomedicine</a>. For example, <a href="Magnetic_resonance_imaging" title="Magnetic resonance imaging">magnetic resonance imaging</a> is widely used in medical imaging of soft tissue and other physiological features which cannot be viewed with traditional x-ray imaging.<a href="#cite_note-yeh-perspective-79">[78]</a>

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<ul><li><a href="Soft_matter" title="Soft matter">Soft matter</a> – Subfield of condensed matter physics</li>

<li><a href="Green%E2%80%93Kubo_relations" title="Green–Kubo relations">Green–Kubo relations</a> – Equation relating transport coefficients to correlation functions</li>

<li><a href="Green's_function_(many-body_theory)" title="Green's function (many-body theory)">Green's function (many-body theory)</a> – Correlators of field operators</li>

<li><a href="Materials_science" title="Materials science">Materials science</a> – Research of materials</li>

<li><a href="Nuclear_spectroscopy" title="Nuclear spectroscopy">Nuclear spectroscopy</a> – Using nucleus properties to probe material properties</li>

<li><a href="Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Comparison of software for molecular mechanics modeling</a></li>

<li><a href="Transparent_materials" class="mw-redirect" title="Transparent materials">Transparent materials</a> – Property of an object or substance to transmit light with minimal scatteringPages displaying short descriptions of redirect targets</li>

<li><a href="Orbital_magnetization" title="Orbital magnetization">Orbital magnetization</a></li>

<li><a href="Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry in quantum mechanics</a> – Properties underlying modern physics</li>

<li><a href="Mesoscopic_physics" title="Mesoscopic physics">Mesoscopic physics</a> – Subdiscipline of condensed matter physics that deals with materials of an intermediate size</li></ul>

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<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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<li id="cite_note-19"><a href="#cite_ref-19">^</a> Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists <a href="Eugene_Wigner" title="Eugene Wigner">Eugene Wigner</a> and <a href="Hillard_Bell_Huntington" title="Hillard Bell Huntington">Hillard Bell Huntington</a> predicted in 1935<a href="#cite_note-metallic-hydrogen-18">[18]</a> that a state <a href="Metallic_hydrogen" title="Metallic hydrogen">metallic hydrogen</a> exists at sufficiently high pressures (over 25 <a href="Pascal_(unit)" title="Pascal (unit)">GPa</a>), but this has not yet been observed.

</li>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Anderson, Philip W. (2018-03-09). Basic Notions Of Condensed Matter Physics. CRC Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-429-97374-1</bdi>.</li>

<li>Girvin, Steven M.; Yang, Kun (2019-02-28). Modern Condensed Matter Physics. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-108-57347-4</bdi>.</li>

<li>Coleman, Piers (2015). Introduction to Many-Body Physics, Cambridge University Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-86488-7</bdi>.</li>

<li>P. M. Chaikin and T. C. Lubensky (2000). Principles of Condensed Matter Physics, Cambridge University Press; 1st edition, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-79450-1</bdi></li>

<li>Alexander Altland and Ben Simons (2006). Condensed Matter Field Theory, Cambridge University Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-84508-4</bdi>.</li>

<li>Michael P. Marder (2010). Condensed Matter Physics, second edition, John Wiley and Sons, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-470-61798-5</bdi>.</li>

<li>Lillian Hoddeson, Ernest Braun, Jürgen Teichmann and Spencer Weart, eds. (1992). Out of the Crystal Maze: Chapters from the History of Solid State Physics, Oxford University Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-505329-X</bdi>.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Condensed_matter_physics" class="extiw external" title="commons:Category:Condensed matter physics">Condensed matter physics</a> at Wikimedia Commons</li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Condensed_matter_physics656" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div id="Condensed_matter_physics656" style="font-size:114%;margin:0 4em"></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="State_of_matter" title="State of matter">States of matter</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Solid" title="Solid">Solid</a></li>

<li><a href="Liquid" title="Liquid">Liquid</a></li>

<li><a href="Plasma_(physics)" title="Plasma (physics)">Plasma</a></li>

<li><a href="Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li>

<li><a href="Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li>

<li><a href="Fermi_gas" title="Fermi gas">Fermi gas</a></li>

<li><a href="Supersolid" title="Supersolid">Supersolid</a></li>

<li><a href="Superfluidity" title="Superfluidity">Superfluid</a></li>

<li><a href="Luttinger_liquid" title="Luttinger liquid">Luttinger liquid</a></li>

<li><a href="Time_crystal" title="Time crystal">Time crystal</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phase phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Order_parameter" class="mw-redirect" title="Order parameter">Order parameter</a></li>

<li><a href="Phase_transition" title="Phase transition">Phase transition</a></li>

<li><a href="Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">Spontaneous symmetry breaking</a></li>

<li><a href="Critical_phenomena" title="Critical phenomena">Critical phenomena</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Electrons in solids</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hall_effect" title="Hall effect">Hall effect</a></li>

<li><a href="Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></li>

<li><a href="Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></li>

<li><a href="Quantum_spin_Hall_effect" title="Quantum spin Hall effect">Quantum spin Hall effect</a></li>

<li><a href="Berry_phase" class="mw-redirect" title="Berry phase">Berry phase</a></li>

<li><a href="Aharonov%E2%80%93Bohm_effect" title="Aharonov–Bohm effect">Aharonov–Bohm effect</a></li>

<li><a href="Josephson_effect" title="Josephson effect">Josephson effect</a></li>

<li><a href="Kondo_effect" title="Kondo effect">Kondo effect</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Drude_model" title="Drude model">Drude model</a></li>

<li><a href="Free_electron_model" title="Free electron model">Free electron model</a></li>

<li><a href="Nearly_free_electron_model" title="Nearly free electron model">Nearly free electron model</a></li>

<li><a href="Bloch's_theorem" title="Bloch's theorem">Bloch's theorem</a></li>

<li><a href="Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid theory</a></li>

<li><a href="Electronic_band_structure" title="Electronic band structure">electronic band structure</a></li>

<li><a href="Anderson_localization" title="Anderson localization">Anderson localization</a></li>

<li><a href="BCS_theory" title="BCS theory">BCS theory</a></li>

<li><a href="Tight_binding_model" class="mw-redirect" title="Tight binding model">tight binding model</a></li>

<li><a href="Hubbard_model" title="Hubbard model">Hubbard model</a></li>

<li><a href="Density_functional_theory" title="Density functional theory">Density functional theory</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Conduction</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li>

<li><a href="Mott_insulator" title="Mott insulator">Mott insulator</a></li>

<li><a href="Semiconductor" title="Semiconductor">Semiconductor</a></li>

<li><a href="Semimetal" title="Semimetal">Semimetal</a></li>

<li><a href="Electrical_conductor" title="Electrical conductor">Conductor</a></li>

<li><a href="Superconductivity" title="Superconductivity">Superconductor</a></li>

<li><a href="Topological_insulator" title="Topological insulator">Topological insulator</a></li>

<li><a href="Spin_gapless_semiconductor" title="Spin gapless semiconductor">Spin gapless semiconductor</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Couplings</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Thermoelectric_effect" title="Thermoelectric effect">Thermoelectricity</a></li>

<li><a href="Piezoelectricity" title="Piezoelectricity">Piezoelectricity</a></li>

<li><a href="Ferroelectricity" title="Ferroelectricity">Ferroelectricity</a></li>

<li><a href="Flexoelectricity" title="Flexoelectricity">Flexoelectricity</a></li>

<li><a href="Electrostriction" title="Electrostriction">Electrostriction</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Magnetic phases</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Amorphous_magnet" title="Amorphous magnet">Amorphous magnet</a></li>

<li><a href="Diamagnetism" title="Diamagnetism">Diamagnet</a></li>

<li><a href="Superdiamagnetism" title="Superdiamagnetism">Superdiamagnet</a></li>

<li><a href="Paramagnetism" title="Paramagnetism">Paramagnet</a></li>

<li><a href="Superparamagnetism" title="Superparamagnetism">Superparamagnet</a></li>

<li><a href="Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li>

<li><a href="Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a></li>

<li><a href="Metamagnetism" title="Metamagnetism">Metamagnet</a></li>

<li><a href="Spin_glass" title="Spin glass">Spin glass</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quasiparticle" title="Quasiparticle">Quasiparticles</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Anyon" title="Anyon">Anyon</a></li>

<li><a href="Bogoliubov_quasiparticle" title="Bogoliubov quasiparticle">Bogoliubov quasiparticle</a></li>

<li><a href="Exciton" title="Exciton">Exciton</a></li>

<li><a href="Magnon" title="Magnon">Magnon</a></li>

<li><a href="Phonon" title="Phonon">Phonon</a></li>

<li><a href="Pines'_demon" title="Pines' demon">Pines' demon</a></li>

<li><a href="Plasmon" title="Plasmon">Plasmon</a></li>

<li><a href="Polariton" title="Polariton">Polariton</a>

<ul><li><a href="Exciton-polariton" title="Exciton-polariton">Exciton-polariton</a></li>

<li><a href="Phonon_polariton" title="Phonon polariton">Phonon polariton</a></li></ul></li>

<li><a href="Polaron" title="Polaron">Polaron</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Soft_matter" title="Soft matter">Soft matter</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Amorphous_solid" title="Amorphous solid">Amorphous solid</a></li>

<li><a href="Granular_material" title="Granular material">Granular matter</a></li>

<li><a href="Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li>

<li><a href="Polymer" title="Polymer">Polymer</a></li>

<li><a href="Interface_and_colloid_science" title="Interface and colloid science">Colloids</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li> Category</li>

<li> <a href="https://commons.wikimedia.org/wiki/Category:Condensed_matter_physics" class="extiw external" title="commons:Category:Condensed matter physics">Commons</a></li>

<li><a href="Portal%3APhysics" title="Portal:Physics">Physics Portal</a></li>

<li> Physics WikiProject</li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Solid_objects288" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Solid_objects288" style="font-size:114%;margin:0 4em">Solid objects</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Objects</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Solids" class="mw-redirect" title="Solids">Solids</a></li>

<li><a href="Physical_object" title="Physical object">Physical object</a></li>

<li><a href="Deformable_bodies" class="mw-redirect" title="Deformable bodies">Deformable bodies</a></li>

<li><a href="Materials" class="mw-redirect" title="Materials">Materials</a></li>

<li><a href="Raw_materials" class="mw-redirect" title="Raw materials">Raw materials</a></li>

<li><a href="Matter" title="Matter">Matter</a></li>

<li><a href="Rigid_body" title="Rigid body">Rigid body</a></li>

<li><a href="Particular" title="Particular">Particular</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="State_of_matter" title="State of matter">State of matter</a></li>

<li><a href="Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li>

<li><a href="Amorphous_solid" title="Amorphous solid">Amorphous solid</a></li>

<li><a href="Bonding_in_solids" title="Bonding in solids">Bonding in solids</a></li>

<li><a href="Miscibility" title="Miscibility">Miscibility</a></li>

<li><a href="Phase_diagram" title="Phase diagram">Phase diagram</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main classes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Metallurgy" title="Metallurgy">Metallurgy</a></li>

<li><a href="Minerals" class="mw-redirect" title="Minerals">Minerals</a></li>

<li><a href="Ceramic_engineering" title="Ceramic engineering">Ceramic engineering</a></li>

<li><a href="Glass_ceramics" class="mw-redirect" title="Glass ceramics">Glass ceramics</a></li>

<li><a href="Polymer_science" title="Polymer science">Polymer science</a> and <a href="Polymer_engineering" title="Polymer engineering">Polymer engineering</a></li>

<li><a href="Composite_materials" class="mw-redirect" title="Composite materials">Composite materials</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Materials_science" title="Materials science">Materials science</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Characterization_(materials_science)" title="Characterization (materials science)">Characterization</a></li>

<li><a href="Computational_materials_science" title="Computational materials science">Computational</a></li>

<li>Fundamental aspects</li>

<li><a href="Materials_informatics" title="Materials informatics">Informatics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Domains</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Condensed-matter_physics" class="mw-redirect" title="Condensed-matter physics">Condensed-matter physics</a></li>

<li><a href="Polymer_physics" title="Polymer physics">Polymer physics</a></li>

<li><a href="Soft_matter" title="Soft matter">Soft-matter physics</a></li>

<li><a href="Solid-state_physics" title="Solid-state physics">Solid-state physics</a></li>

<li><a href="Crystallography" title="Crystallography">Crystallography</a></li>

<li><a href="Surface_science" title="Surface science">Surface science</a></li>

<li><a href="Tribology" title="Tribology">Tribology</a></li>

<li><a href="Microelectronics" title="Microelectronics">Microelectronics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Interdisciplinarity" title="Interdisciplinarity">Interdisciplinary</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Solid-state_chemistry" title="Solid-state chemistry">Solid-state chemistry</a></li>

<li><a href="Polymer_chemistry" title="Polymer chemistry">Polymer chemistry</a></li>

<li><a href="Mineralogy" title="Mineralogy">Mineralogy</a></li>

<li><a href="Mining_engineering" title="Mining engineering">Mining engineering</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li> Category</li>

<li> <a href="https://commons.wikimedia.org/wiki/Category:Materials_science" class="extiw external" title="commons:Category:Materials science">Common</a></li>

<li><a href="Material" title="Material">Material</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Major_branches_of_physics48" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Major_branches_of_physics48" style="font-size:114%;margin:0 4em">Major <a href="Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Applied_physics" title="Applied physics">Applied</a>

<ul><li><a href="Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Experimental_physics" title="Experimental physics">Experimental</a></li>

<li><a href="Theoretical_physics" title="Theoretical physics">Theoretical</a>

<ul><li><a href="Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Classical_mechanics" title="Classical mechanics">Classical mechanics</a>

<ul><li><a href="Newton's_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li>

<li><a href="Analytical_mechanics" title="Analytical mechanics">Analytical</a></li>

<li><a href="Celestial_mechanics" title="Celestial mechanics">Celestial</a></li>

<li><a href="Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li>

<li><a href="Acoustics" title="Acoustics">Acoustics</a></li>

<li><a href="Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li>

<li><a href="Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a>

<li><a href="Thermodynamics" title="Thermodynamics">Thermodynamics</a>

<ul><li><a href="Statistical_mechanics" title="Statistical mechanics">Statistical</a></li>

<li><a href="Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a>

<ul><li><a href="Special_relativity" title="Special relativity">Special</a></li>

<li><a href="General_relativity" title="General relativity">General</a></li></ul></li>

<li><a href="Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li>

<li><a href="Particle_physics" title="Particle physics">Particle physics</a></li>

<li><a href="Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li>

<li><a href="Atomic%2C_molecular%2C_and_optical_physics" title="Atomic, molecular, and optical physics">Atomic, molecular, and optical physics</a>

<ul><li><a href="Atomic_physics" title="Atomic physics">Atomic</a></li>

<li><a href="Molecular_physics" title="Molecular physics">Molecular</a></li>

<li><a href="Optics#Modern_optics" title="Optics">Modern optics</a></li></ul></li>

<li>

<ul><li><a href="Solid-state_physics" title="Solid-state physics">Solid-state physics</a></li>

<li><a href="Crystallography" title="Crystallography">Crystallography</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Interdisciplinary</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Astrophysics" title="Astrophysics">Astrophysics</a></li>

<li><a href="Atmospheric_physics" title="Atmospheric physics">Atmospheric physics</a></li>

<li><a href="Biophysics" title="Biophysics">Biophysics</a></li>

<li><a href="Chemical_physics" title="Chemical physics">Chemical physics</a></li>

<li><a href="Geophysics" title="Geophysics">Geophysics</a></li>

<li><a href="Materials_science" title="Materials science">Materials science</a></li>

<li><a href="Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li>

<li><a href="Medical_physics" title="Medical physics">Medical physics</a></li>

<li><a href="Physical_oceanography" title="Physical oceanography">Ocean physics</a></li>

<li><a href="Quantum_information_science" title="Quantum information science">Quantum information science</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_physics" title="History of physics">History of physics</a></li>

<li><a href="Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a></li>

<li><a href="Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li>

<li><a href="Physics_education" title="Physics education">Physics education</a>

<ul><li><a href="Physics_education_research" title="Physics education research">research</a></li></ul></li>

<li><a href="Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">Timeline of physics discoveries</a></li></ul>

</div></td></tr></tbody></table></div>

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