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{{Condensed matter physics}}
'''Condensed matter physics''' is the field of [[physics]] that deals with the macroscopic and microscopic physical properties of [[matter]], especially the [[solid]] and [[liquid]] [[State of matter|phases]], that arise from [[electromagnetic]] forces between [[atom]]s and [[electrons]]. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the [[superconductivity|superconducting]] phase exhibited by certain materials at extremely low [[cryogenic]] [[temperature]]s, the [[ferromagnet]]ic and [[antiferromagnet]]ic phases of [[Spin (physics)|spins]] on [[crystal lattice]]s of atoms, the [[Bose–Einstein condensates]] found in [[ultracold atom]]ic systems, and [[liquid crystals]]. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the [[physical law]]s of [[quantum mechanics]], [[electromagnetism]], [[statistical mechanics]], and other [[theoretical physics|physics theories]] to develop mathematical models and predict the properties of extremely large groups of atoms.<ref>{{cite web|url=https://physics.yale.edu/research/condensed-matter-physics-theory|title=Condensed Matter Physics Theory|website=Yale University Physics Department|access-date= 2023-11-30}}</ref>
The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists,<ref>{{cite web|url= http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-url= https://web.archive.org/web/20090327141400/http://www.physicstoday.org/jobs/seek/condensed_matter.html|archive-date= 2009-03-27|website=Physics Today Jobs|title= Condensed Matter Physics Jobs: Careers in Condensed Matter Physics|access-date= 2010-11-01}}</ref> and the Division of Condensed Matter Physics is the largest division of the [[American Physical Society]].<ref name=aps-history>{{cite web|title=History of Condensed Matter Physics|url=http://www.aps.org/units/dcmp/history.cfm|publisher=American Physical Society|access-date=27 March 2012}}</ref> These include solid state and [[soft matter]] physicists, who study [[quantum mechanics|quantum]] and non-quantum physical properties of matter respectively.<ref>{{cite web|title=Condensed Matter Physics|url=https://www.colorado.edu/physics/research/condensed-matter-physics |website=University of Colorado Boulder Physics Department|date=26 April 2016 |access-date=2023-11-30}}</ref> Both types study a great range of materials, providing many research, funding and employment opportunities.<ref>{{cite web|title=Condensed Matter and Materials Physics|url=https://physics.uiowa.edu/research/condensed-matter-and-materials-physics|website=Iowa College of Liberal Arts and Sciences|access-date=2023-11-30}}</ref> The field overlaps with [[chemistry]], [[materials science]], [[engineering]] and [[nanotechnology]], and relates closely to [[atomic physics]] and [[biophysics]]. The [[theoretical physics]] of condensed matter shares important concepts and methods with that of [[particle physics]] and [[nuclear physics]].<ref name=marvincohen2008>{{cite journal|last=Cohen|first=Marvin L.|title=Essay: Fifty Years of Condensed Matter Physics|journal=Physical Review Letters|year=2008|volume=101|issue=25|doi=10.1103/PhysRevLett.101.250001|url=http://prl.aps.org/edannounce/PhysRevLett.101.250001|access-date=31 March 2012|bibcode= 2008PhRvL.101y0001C|pmid=19113681|page=250001}}</ref>
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==Etymology==
According to physicist [[Philip Warren Anderson]], the use of the term "condensed matter" to designate a field of study was coined by him and [[Volker Heine]], when they changed the name of their group at the [[Cavendish Laboratories]], [[Cambridge]], from ''Solid state theory'' to ''Theory of Condensed Matter'' in 1967,<ref name=pwa-princeton>{{cite web|title=Philip Anderson|url=http://www.princeton.edu/physics/people/display_person.xml?netid=pwa&display=faculty |website=Department of Physics|publisher=Princeton University|access-date=27 March 2012}}</ref> as they felt it better included their interest in liquids, [[nuclear matter]], and so on.<ref name=wsn>{{cite journal|title=In Focus: More and Different|url=http://www.worldscientific.com/newsletter/newsletter/nov11n33p02.shtml|journal=World Scientific Newsletter|date=November 2011|volume=33 |page=2|last = Anderson|first = Philip W.}}</ref><ref>{{Cite book|last=Anderson|first=Philip W.|url=https://books.google.com/books?id=9HhQDwAAQBAJ|title=Basic Notions Of Condensed Matter Physics|date=2018-03-09|publisher=CRC Press|isbn=978-0-429-97374-1|language=en}}</ref> Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the [[Springer Science+Business Media|Springer-Verlag]] journal ''Physics of Condensed Matter'', launched in 1963.<ref>{{cite web|url=https://books.google.com/books?id=dTsgAAAAIAAJ|title=''Physics of Condensed Matter''|volume=1|access-date=20 April 2015|year=1963}}</ref> The name "condensed matter physics" emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, whereas "solid state physics" was often associated with restricted industrial applications of metals and semiconductors. In the 1960s and 70s, some physicists felt the more comprehensive name better fit the funding environment and [[Cold War]] politics of the time.<ref name=martin-pip>{{cite journal|last=Martin|first=Joseph D. |title=What's in a Name Change? Solid State Physics, Condensed Matter Physics, and Materials Science|journal=Physics in Perspective |date=2015|volume=17|issue= 1|doi=10.1007/s00016-014-0151-7|pages=3–32|bibcode= 2015PhP....17....3M|s2cid=117809375 |url=http://dro.dur.ac.uk/29168/1/29168.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://dro.dur.ac.uk/29168/1/29168.pdf |archive-date=2022-10-09 |url-status=live }}</ref>
References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book ''Kinetic Theory of Liquids'',<ref name=Frenkel>{{cite book|last=Frenkel|first=J.|title=Kinetic Theory of Liquids|year=1947|publisher=Oxford University Press}}</ref> [[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==
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One of the first studies of condensed states of matter was by [[People of England|English]] [[chemist]] [[Humphry Davy]], in the first decades of the nineteenth century. Davy observed that of the forty [[chemical element]]s known at the time, twenty-six had [[metal]]lic properties such as [[lustre (mineralogy)|lustre]], [[ductility]] and high electrical and thermal conductivity.<ref name=goodstein>{{cite journal|last1=Goodstein|first1=David|author1-link=David Goodstein|last2=Goodstein|first2=Judith|author2-link=Judith R. Goodstein|title=Richard Feynman and the History of Superconductivity|journal=Physics in Perspective|year=2000|volume=2|issue=1|url=http://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|access-date=7 April 2012|doi=10.1007/s000160050035|pages=30|bibcode=2000PhP.....2...30G|s2cid=118288008|archive-url=https://web.archive.org/web/20151117113759/https://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|archive-date=17 November 2015|url-status=dead}}</ref> This indicated that the atoms in [[John Dalton]]'s [[atomic theory]] were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as [[nitrogen]] and [[hydrogen]] could be liquefied under the right conditions and would then behave as metals.<ref name=davy-1839>{{cite book |editor-last=Davy |editor-first = John |title=The collected works of Sir Humphry Davy: Vol. II |year=1839|publisher=Smith Elder & Co., Cornhill |url = https://archive.org/details/bub_gb_6WNKAAAAYAAJ |page=[https://archive.org/details/bub_gb_6WNKAAAAYAAJ/page/n34 22] }}</ref>{{NoteTag|Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists [[Eugene Wigner]] and [[Hillard Bell Huntington]] predicted in 1935<ref name=metallic-hydrogen>{{cite journal |last=Silvera|first=Isaac F.|author2=Cole, John W. |title=Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist|journal=Journal of Physics|year=2010|volume=215|issue=1 |doi=10.1088/1742-6596/215/1/012194 |bibcode= 2010JPhCS.215a2194S |pages=012194 |url = http://nrs.harvard.edu/urn-3:HUL.InstRepos:9569212 |doi-access=free}}</ref> that a state [[metallic hydrogen]] exists at sufficiently high pressures (over 25 [[Pascal (unit)|GPa]]), but this has not yet been observed.}}
In 1823, [[Michael Faraday]], then an assistant in Davy's lab, successfully liquefied [[chlorine]] and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and [[oxygen]].<ref name=goodstein /> Shortly after, in 1869, [[People of Ireland|Irish]] chemist [[Thomas Andrews (scientist)|Thomas Andrews]] studied the [[phase transition]] from a liquid to a gas and coined the term [[Critical point (thermodynamics)|critical point]] to describe the condition where a gas and a liquid were indistinguishable as phases,<ref name=thomasandrews>{{cite journal|last=Rowlinson|first=J. S.|title=Thomas Andrews and the Critical Point|journal=Nature|year=1969|volume=224|issue=8|doi=10.1038/224541a0|pages=541–543|bibcode= 1969Natur.224..541R|s2cid=4168392}}</ref> and [[Netherlands|Dutch]] physicist [[Johannes van der Waals]] supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.<ref name=atkins>{{cite book|last1=Atkins|first1=Peter|last2=de Paula|first2=Julio|title=Elements of Physical Chemistry|year=2009|publisher=Oxford University Press|isbn=978-1-4292-1813-9}}</ref>{{rp|35–38}} By 1908, [[James Dewar]] and [[Heike Kamerlingh Onnes]] were successfully able to liquefy hydrogen and the then newly discovered [[helium]]
[[Paul Drude]] in 1900 proposed the first theoretical model for a classical [[electron]] moving through a metallic solid.<ref name=marvincohen2008 /> Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the [[Wiedemann–Franz law]].<ref name="Kittel 1996">{{cite book|last=Kittel|first=Charles|title=[[Introduction to Solid State Physics]]|year=1996|publisher=John Wiley & Sons|isbn=978-0-471-11181-8}}</ref><ref name=Hoddeson-1992>{{cite book|last=Hoddeson|first=Lillian|title=Out of the Crystal Maze: Chapters from The History of Solid State Physics|year=1992|publisher=Oxford University Press|isbn=978-0-19-505329-6|url=https://books.google.com/books?id=WCpPPHhMdRcC&pg=PA29}}</ref>{{rp|27–29}} However, despite the success of [[Drude model|Drude's model]], it had one notable problem: it was unable to correctly explain the electronic contribution to the [[specific heat]] and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.<ref name=Kragh2002>{{cite book |last= Kragh |first= Helge |title= Quantum Generations: A History of Physics in the Twentieth Century |publisher= Princeton University Press |edition= Reprint |date= 2002 |isbn= 978-0-691-09552-3}}</ref>{{rp|366–368}}
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===Advent of quantum mechanics===
Drude's classical model was augmented by [[Wolfgang Pauli]], [[Arnold Sommerfeld]], [[Felix Bloch]] and other physicists. Pauli realized that the free electrons in metal must obey the [[Fermi–Dirac statistics]]. Using this idea, he developed the theory of [[paramagnetism]] in 1926. Shortly after, Sommerfeld incorporated the [[Fermi–Dirac statistics]] into the [[free electron model]] and made it better to explain the heat capacity. Two years later, Bloch used [[quantum mechanics]] to describe the motion of an electron in a periodic lattice.<ref name=Kragh2002/>{{rp|366–368}}
The mathematics of crystal structures developed by [[Auguste Bravais]], [[Yevgraf Fyodorov]] and others was used to classify crystals by their [[symmetry group]], and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935.<ref name=Aroyo-2006>{{Cite book|last=Aroyo|first=Mois, I.|author2=Müller, Ulrich|author3=Wondratschek, Hans|title=Historical introduction|year=2006|volume=A|pages=2–5|doi=10.1107/97809553602060000537|series=International Tables for Crystallography|isbn=978-1-4020-2355-2|url=http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|citeseerx=10.1.1.471.4170|access-date=2017-10-24|archive-date=2008-10-03|archive-url=https://web.archive.org/web/20081003122816/http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|url-status=dead}}</ref> [[Band theory|Band structure calculations]] [[File:Replica-of-first-transistor.jpg|thumb|left|A replica of the first [[point-contact transistor]] in [[Bell labs]]]]
In 1879, [[Edwin Herbert Hall]] working at the [[Johns Hopkins University]] discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.<ref>{{cite journal|title=On a New Action of the Magnet on Electric Currents|author=Hall, Edwin|journal=American Journal of Mathematics|volume=2|year=1879|pages=287–92|url=http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|access-date=2008-02-28|doi=10.2307/2369245|issue=3|jstor=2369245|s2cid=107500183 |url-status=dead|archive-url=https://web.archive.org/web/20070208040346/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|archive-date=2007-02-08}}</ref> This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the [[Hall effect]], but it was not properly explained at the time
Magnetism as a property of matter has been known in China since 4000 BC.<ref name=mattis-magnetism-2006>{{cite book|last=Mattis|first=Daniel|title=The Theory of Magnetism Made Simple|year=2006|publisher=World Scientific|isbn=978-981-238-671-7}}</ref>{{rp|1–2}} However, the first modern studies of magnetism only started with the development of [[electrodynamics]] by Faraday, [[James Clerk Maxwell|Maxwell]] and others in the nineteenth century, which included classifying materials as [[ferromagnetic]], [[paramagnetic]] and [[diamagnetic]] based on their response to magnetization.<ref name=Chatterjee-2004-ferromagnetism>{{cite journal|last=Chatterjee|first=Sabyasachi|title=Heisenberg and Ferromagnetism|journal=Resonance|date=August 2004|volume=9|issue=8|doi=10.1007/BF02837578|url=http://www.ias.ac.in/describe/article/reso/009/08/0057-0066|access-date=13 June 2012|pages=57–66|s2cid=123099296}}</ref> [[Pierre Curie]] studied the dependence of magnetization on temperature and discovered the [[Curie point]] phase transition in ferromagnetic materials.<ref name=mattis-magnetism-2006 /> In 1906, [[Pierre Weiss]] introduced the concept of [[magnetic domain]]s to explain the main properties of ferromagnets.<ref name=Visintin-domains>{{cite book|last=Visintin|first=Augusto|title=Differential Models of Hysteresis|year=1994|publisher=Springer|isbn=978-3-540-54793-8|url=https://books.google.com/books?id=xZrTIDmNOlgC&pg=PA9}}</ref>{{rp|9}} The first attempt at a microscopic description of magnetism was by [[Wilhelm Lenz]] and [[Ernst Ising]] through the [[Ising model]] that described magnetic materials as consisting of a periodic lattice of [[Spin (physics)|spins]] that collectively acquired magnetization.<ref name=mattis-magnetism-2006/> The Ising model was solved exactly to show that [[spontaneous magnetization]]
===Modern many-body physics===
[[File:Meissner effect p1390048.jpg|thumb|left|200px|alt=A magnet levitating over a superconducting material.|A [[magnet]] [[Meissner effect|levitating]] above a [[high-temperature superconductor]]. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.<ref>{{cite journal |last1= Merali |first1= Zeeya |title= Collaborative physics: string theory finds a bench mate |journal= Nature |volume= 478 |pages= 302–304 |year= 2011 |doi= 10.1038/478302a |pmid= 22012369 |issue= 7369|bibcode= 2011Natur.478..302M|doi-access= free }}</ref>]]
The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of [[superconductivity]] and the [[Kondo effect]].<ref name=Coleman-2003>{{cite journal|last=Coleman|first=Piers|title=Many-Body Physics: Unfinished Revolution|journal=Annales Henri Poincaré|year=2003|volume=4|issue=2|doi=10.1007/s00023-003-0943-9|arxiv=cond-mat/0307004|bibcode= 2003AnHP....4..559C|pages=559–580|citeseerx=10.1.1.242.6214|s2cid=8171617}}</ref> After [[World War II]], several ideas from quantum field theory were applied to condensed matter problems. These included recognition of [[collective excitation]] modes of solids and the important notion of a quasiparticle.
[[File:Quantum Hall effect - Russian.png|thumb|right|The [[quantum Hall effect]]: Components of the Hall resistivity as a function of the external magnetic field<ref name="von Klitzing"/>{{rp|fig. 14}}]]
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A major revolution came in the field of [[crystallography]] with the discovery of [[quasicrystal]]s by [[Daniel Shechtman]]. In 1982 Shechtman observed that certain metallic [[alloy]]s produce unusual diffractograms that indicated that their crystalline structures are ordered, but lack [[translational symmetry]]. The discovery led the [[International Union of Crystallography]] to change its definition of a crystal to account for aperiodic structures.<ref name=bloomberg>{{cite news |url = https://www.bloomberg.com/news/2011-10-05/technion-s-shechtman-wins-chemistry-nobel-for-discovery-of-quasicrystals.html |title=Tecnion's Shechtman Wins Nobel in Chemistry for Quasicrystals Discovery |last = Gerlin |first = Andrea |date= 5 October 2011|work=Bloomberg}}</ref> The second half of the twentieth century was also important for the development of [[soft condensed matter]], in particular the [[thermodynamic equilibrium]] of several soft-matter systems such as polymers and liquid crystals due to [[Paul Flory|Flory]], [[Pierre de Gennes|de Gennes]] and others.<ref name=Cates-2004-soft>{{cite journal |last=Cates |first=M. E. |title=Soft Condensed Matter (Materia Condensata Soffice) |year=2004 |arxiv=cond-mat/0411650 |bibcode= 2004cond.mat.11650C |page = 11650 }}</ref> -->
In 1986, [[Karl Alexander Müller|Karl Müller]] and [[Johannes Bednorz]] discovered the first [[high temperature superconductor]],
<!--
The 1986 discovery of [[high temperature superconductivity]] generated interest in the study of [[strongly correlated materials]].<ref name=bouvier-2010>{{cite journal|last=Bouvier|first=Jacqueline|author2=Bok, Julien |title=Electron–Phonon Interaction in the High-T<sub>C</sub> Cuprates in the Framework of the Van Hove Scenario|journal=Advances in Condensed Matter Physics|year=2010|volume=2010|doi=10.1155/2010/472636|pages=472636}}</ref> Modern research in condensed matter physics is focused on problems in strongly correlated materials, [[quantum phase transitions]] and applications of [[quantum field theory]] to condensed matter systems. Problems of current interest include description of high temperature superconductivity, [[topological order]], and other novel materials such as [[graphene]] and [[carbon nanotube]]s.<ref name=yeh-perspective />
-->
In 2012, several groups released preprints which suggest that [[Samarium#Samarium hexaboride|samarium hexaboride]] has the properties of a [[topological insulator]]<ref name="Nature-1">{{cite journal|journal=[[Nature (journal)|Nature]]|volume=492|issue=7428|pages=165|title=Hopes surface for exotic insulator|author=Eugenie Samuel Reich|doi=10.1038/492165a|pmid=23235853|year=2012|bibcode=2012Natur.492..165S|doi-access=free}}</ref> in accord with the earlier theoretical predictions.<ref name="TKI">{{Cite journal| doi= 10.1103/PhysRevLett.104.106408| pmid= 20366446| volume= 104| issue= 10| pages= 106408| last= Dzero| first= V.|author2=K. Sun |author3=V. Galitski |author4=P. Coleman |title= Topological Kondo Insulators| journal= Physical Review Letters| year= 2010|arxiv= 0912.3750 |bibcode= 2010PhRvL.104j6408D| s2cid= 119270507}}</ref> Since samarium hexaboride is an established [[Kondo insulator]], i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.
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The metallic state has historically been an important building block for studying properties of solids.<ref name="AshcroftMermin1976"/> The first theoretical description of metals was given by [[Paul Drude]] in 1900 with the [[Drude model]], which explained electrical and thermal properties by describing a metal as an [[ideal gas]] of then-newly discovered [[electron]]s. He was able to derive the empirical [[Wiedemann-Franz law]] and get results in close agreement with the experiments.<ref name=Hoddeson-1992/>{{rp|90–91}} This classical model was then improved by [[Arnold Sommerfeld]] who incorporated the [[Fermi–Dirac statistics]] of electrons and was able to explain the anomalous behavior of the [[specific heat]] of metals in the [[Wiedemann–Franz law]].<ref name=Hoddeson-1992/>{{rp|101–103}} In 1912, The structure of crystalline solids was studied by [[Max von Laue]] and Paul Knipping, when they observed the [[X-ray diffraction]] pattern of crystals, and concluded that crystals get their structure from periodic [[lattice model (physics)|lattices]] of atoms.<ref name=Hoddeson-1992/>{{rp|48}}<ref>{{cite journal|last=Eckert|first=Michael|title=Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions|journal=Acta Crystallographica A|year=2011|volume=68|issue=1|doi=10.1107/S0108767311039985|pmid=22186281|url=http://journals.iucr.org/a/issues/2012/01/00/wx0005/index.html|bibcode= 2012AcCrA..68...30E|pages=30–39|doi-access=free}}</ref> In 1928, Swiss physicist [[Felix Bloch]] provided a wave function solution to the [[Schrödinger equation]] with a [[Periodic function|periodic]] potential, known as [[Bloch's theorem]].<ref name=han-2010>{{cite book|last=Han|first=Jung Hoon|title=Solid State Physics|year=2010|publisher=Sung Kyun Kwan University|url=http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|url-status=dead|archive-url=https://web.archive.org/web/20130520224858/http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|archive-date=2013-05-20}}</ref>
Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions.<ref name=perdew-2010>{{cite journal|last=Perdew|first=John P.|author2=Ruzsinszky, Adrienn|author2-link=Adrienn Ruzsinszky |title=Fourteen Easy Lessons in Density Functional Theory|journal=International Journal of Quantum Chemistry|year=2010|volume=110|pages=2801–2807|url=http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-date=2022-10-09 |url-status=live|access-date=13 May 2012|doi=10.1002/qua.22829|issue=15|doi-access=free}}</ref> The [[Thomas–Fermi model|Thomas–Fermi theory]], developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a [[Variational method|variational parameter]]. Later in the 1930s, [[Douglas Hartree]], [[Vladimir Fock]] and [[John C. Slater|John Slater]] developed the so-called [[Hartree–Fock method|Hartree–Fock wavefunction]] as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for [[Exchange symmetry|exchange statistics]] of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly.<ref name="AshcroftMermin1976">{{cite book|author1=Neil W. Ashcroft|author2=N. David Mermin|title=Solid state physics|year=1976|publisher=Saunders College|isbn=978-0-03-049346-1}}</ref>{{rp|330–337}} Finally in 1964–65, [[Walter Kohn]], [[Pierre Hohenberg]] and [[Lu Jeu Sham]] proposed the [[density functional theory]] (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.<ref name=perdew-2010 />
===Symmetry breaking===
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{{Main|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]], [[pressure]], or [[molar composition]]. In a single-component system, a classical phase transition occurs at a temperature (at a specific pressure) where there is an abrupt change in the order of the system
In [[quantum phase transition]]s, 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 fluctuation]]s originating from the [[Heisenberg uncertainty principle]]. Here, the different quantum phases of the system refer to distinct [[ground state]]s 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.<ref name=Vojta2003/>
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==Experimental==
Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of [[electric field|electric]] and [[magnetic field]]s, measuring [[response function]]s, [[transport theory (statistical physics)|transport properties]] and [[thermometry]].<ref name=exptcm>{{cite book|last=Richardson|first=Robert C.|title=Experimental methods in Condensed Matter Physics at Low Temperatures|year=1988|publisher=Addison-Wesley|isbn=978-0-201-15002-5}}</ref> Commonly used experimental methods include [[spectroscopy]], with probes such as [[X-ray spectroscopy|X-rays]], [[infrared spectroscopy|infrared light]] and [[inelastic neutron scattering]]; study of thermal response, such as [[specific heat]] and measuring transport via thermal and heat [[conduction (heat)|conduction]].
[[File:Lysozym diffraction.png|thumb|upright|Image of X-ray diffraction pattern from a [[protein]] crystal
===Scattering===
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In experimental condensed matter physics, external [[magnetic field]]s act as [[thermodynamic variable]]s that control the state, phase transitions and properties of material systems.<ref name=iupap-report>{{cite web |last=Committee on Facilities for Condensed Matter Physics|title=Report of the IUPAP working group on Facilities for Condensed Matter Physics : High Magnetic Fields |url=http://archive.iupap.org/wg/wg3/hmff/file_50963.pdf |publisher=International Union of Pure and Applied Physics|year=2004 |quote=The magnetic field is not simply a spectroscopic tool but a thermodynamic variable which, along with temperature and pressure, controls the state, the phase transitions and the properties of materials.|access-date=2016-02-07|archive-url=https://web.archive.org/web/20140222151520/http://www.iupap.org/wg/wg3/hmff/file_50963.pdf|archive-date=2014-02-22|url-status=dead }}</ref> [[Nuclear magnetic resonance]] (NMR) is a method by which external [[magnetic fields]] are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60 [[Tesla (unit)|tesla]]. Higher magnetic fields can improve the quality of NMR measurement data.<ref name="StatesAstronomy2013"/>{{rp|69}}<ref>{{cite book|title=High Magnetic Fields|chapter=Nuclear Magnetic Resonance in Solids at very high magnetic fields|author1=Moulton, W. G. |author2=Reyes, A. P. |editor=Herlach, Fritz |series=Science and Technology|publisher=World Scientific|year=2006|chapter-url=https://books.google.com/books?id=tN8CbCHzBmcC&pg=PA185|isbn=978-981-277-488-0}}</ref>{{rp|185}} [[Quantum oscillations]] is another experimental method where high magnetic fields are used to study material properties such as the geometry of the [[Fermi surface]].<ref name=doiron-leyraud2007>{{cite journal|last=Doiron-Leyraud|first=Nicolas|title=Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor|journal=Nature|year=2007|volume=447|pages=565–568|doi=10.1038/nature05872|arxiv= 0801.1281 |bibcode= 2007Natur.447..565D|issue=7144|pmid=17538614 |s2cid=4397560|display-authors=etal}}</ref> High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized [[magnetoelectric effect]], image [[magnetic monopole]], and the half-integer [[quantum Hall effect]].<ref name="StatesAstronomy2013">{{cite book|author=Committee to Assess the Current Status and Future Direction of High Magnetic Field Science in the United States; Board on Physics and Astronomy; Division on Engineering and Physical Sciences; National Research Council|title=High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions|url=http://www.nap.edu/catalog/18355/high-magnetic-field-science-and-its-application-in-the-united-states|date=25 November 2013|publisher=National Academies Press|isbn=978-0-309-28634-3|doi=10.17226/18355}}</ref>{{rp|57}}
===
The [[local structure]], as well as the structure of the nearest neighbour atoms,
===Cold atomic gases===
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[[File:Fullerene Nanogears - GPN-2000-001535.jpg|thumb|right|Computer simulation of ''nanogears'' made of [[fullerene]] molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.]]
Research in condensed matter physics<ref name=":0" /><ref>{{cite book|url=https://www.cambridge.org/core/books/introduction-to-manybody-physics/B7598FC1FCEE0285F5EC767E835854C8|title=Introduction to Many-Body Physics|last=Coleman|first=Piers|date=2015|publisher=Cambridge Core|doi=10.1017/CBO9781139020916 |isbn=9780521864886 |language=en|access-date=2020-04-20}}</ref> has given rise to several device applications, such as the development of the [[semiconductor]] [[transistor]],<ref name=marvincohen2008 /> [[laser]] technology,<ref name=NRC1986 /> [[magnetic storage]], [[liquid crystals]], [[optical fibres]]<ref>{{cite web|title=Condensed Matter|url=https://live-sas-physics.pantheon.sas.upenn.edu/research/condensed-matter|website=Physics Pantheon|access-date=2023-11-30}}</ref> and several phenomena studied in the context of [[nanotechnology]].<ref name="2010Committee2007">{{cite book|author=Committee on CMMP 2010; Solid State Sciences Committee; Board on Physics and Astronomy; Division on Engineering and Physical Sciences, National Research Council|title=Condensed-Matter and Materials Physics: The Science of the World Around Us|url=http://www.nap.edu/catalog/11967/condensed-matter-and-materials-physics-the-science-of-the-world|date=21 December 2007|publisher=National Academies Press|isbn=978-0-309-13409-5|doi=10.17226/11967}}</ref>{{rp|111ff}} Methods such as [[Scanning tunneling microscope|scanning-tunneling microscopy]] can be used to control processes at the [[nanometer]] scale, and have given rise to the study of nanofabrication.<ref name=yeh-perspective>{{cite journal |last=Yeh|first=Nai-Chang |title=A Perspective of Frontiers in Modern Condensed Matter Physics |journal=AAPPS Bulletin|year=2008|volume=18|issue=2 |url = https://yehgroup.caltech.edu/files/2016/08/AAPPS_v18_no2_pg11.pdf |access-date=19 June 2018}}</ref> Such molecular machines were developed for example by Nobel
In [[quantum computation]], information is represented by quantum bits, or [[qubit]]s. The qubits may [[quantum decoherence|decohere]] quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, including [[Josephson junction]] qubits, [[spintronic]] qubits using the [[Spin (physics)|spin]] orientation of magnetic materials,
Condensed matter physics also has important uses for [[biomedicine]]
== See also ==
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{{Condensed matter physics topics}}
{{Solid objects}}
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