Editing Condensed matter physics (section)

===Modern many-body physics===
[[File:Meissner effect p1390048.jpg|thumb|left|200px|alt=A magnet levitating over a superconducting material.|A [[magnet]] [[Meissner effect|levitating]] above a [[high-temperature superconductor]]. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.<ref>{{cite journal |last1= Merali |first1= Zeeya |title= Collaborative physics: string theory finds a bench mate |journal= Nature |volume= 478 |pages= 302–304 |year= 2011 |doi= 10.1038/478302a |pmid= 22012369 |issue= 7369|bibcode= 2011Natur.478..302M|doi-access= free }}</ref>]]
The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of [[superconductivity]] and the [[Kondo effect]].<ref name=Coleman-2003>{{cite journal|last=Coleman|first=Piers|title=Many-Body Physics: Unfinished Revolution|journal=Annales Henri Poincaré|year=2003|volume=4|issue=2|doi=10.1007/s00023-003-0943-9|arxiv=cond-mat/0307004|bibcode= 2003AnHP....4..559C|pages=559–580|citeseerx=10.1.1.242.6214|s2cid=8171617}}</ref> After [[World War II]], several ideas from quantum field theory were applied to condensed matter problems. These included recognition of [[collective excitation]] modes of solids and the important notion of a quasiparticle. Soviet physicist [[Lev Landau]] used the idea for the [[Fermi liquid theory]] wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.<ref name=Coleman-2003/> Landau also developed a [[mean-field theory]] for continuous phase transitions, which described ordered phases as [[Spontaneous symmetry breaking|spontaneous breakdown of symmetry]]. The theory also introduced the notion of an [[order parameter]] to distinguish between ordered phases.<ref name=Kadanoff-2009>{{cite book|last=Kadanoff|first=Leo, P.|title=Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena|year=2009|publisher=The University of Chicago|url=http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf|access-date=2012-06-14|archive-date=2015-12-31|archive-url=https://web.archive.org/web/20151231215516/http://jfi.uchicago.edu/~leop/RejectedPapers/ExtraV1.2.pdf|url-status=dead}}</ref> Eventually in 1956, [[John Bardeen]], [[Leon Cooper]] and [[Robert Schrieffer]] developed the so-called [[BCS theory]] of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by [[phonon]]s in the lattice can give rise to a bound state called a [[Cooper pair]].<ref name=coleman />
[[File:Quantum Hall effect - Russian.png|class=skin-invert-image|thumb|right|The [[quantum Hall effect]]: Components of the Hall resistivity as a function of the external magnetic field<ref name="von Klitzing"/>{{rp|fig. 14}}]]

The study of phase transitions and the critical behavior of observables, termed [[critical phenomena]], was a major field of interest in the 1960s.<ref name=Fisher-rmp-1998>{{cite journal|last=Fisher|first=Michael E.|title=Renormalization group theory: Its basis and formulation in statistical physics|journal=Reviews of Modern Physics|year=1998|volume=70|issue=2|doi=10.1103/RevModPhys.70.653|bibcode= 1998RvMP...70..653F|pages=653–681|citeseerx=10.1.1.129.3194}}</ref> [[Leo Kadanoff]], [[Benjamin Widom]] and [[Michael Fisher]] developed the ideas of [[critical exponent]]s and [[widom scaling]]. These ideas were unified by [[Kenneth G. Wilson]] in 1972, under the formalism of the [[renormalization group]] in the context of quantum field theory.<ref name=Fisher-rmp-1998/>

The [[quantum Hall effect]] was discovered by [[Klaus von Klitzing]], Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant <math>e^2/h</math>.(see figure) The effect was observed to be independent of parameters such as system size and impurities.<ref name="von Klitzing">{{cite web |url= https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.nobelprize.org/nobel_prizes/physics/laureates/1985/klitzing-lecture.pdf |archive-date=2022-10-09 |url-status=live |title= The Quantized Hall Effect |last= von Klitzing |first= Klaus |date= 9 Dec 1985 |website= Nobelprize.org}}</ref>  In 1981, theorist [[Robert Laughlin]] proposed a theory explaining the unanticipated precision of the integral plateau.  It also implied that the Hall conductance is proportional to a topological invariant, called [[Chern class#Chern numbers|Chern number]], whose relevance for the band structure of solids was formulated by [[David J. Thouless]] and collaborators.<ref name="Avron-hall-2003">{{cite journal|last=Avron|first=Joseph E. |author2=Osadchy, Daniel |author3=Seiler, Ruedi |title=A Topological Look at the Quantum Hall Effect|journal=Physics Today|year=2003|volume=56|issue=8|doi=10.1063/1.1611351|bibcode= 2003PhT....56h..38A|pages=38–42|doi-access=free}}</ref><ref name="Thouless1998">{{cite book|author=David J Thouless|title=Topological Quantum Numbers in Nonrelativistic Physics|date=12 March 1998|publisher=World Scientific|isbn=978-981-4498-03-6}}</ref>{{rp|69, 74}} Shortly after, in 1982, [[Horst Störmer]] and [[Daniel Tsui]] observed the [[fractional quantum Hall effect]] where the conductance was now a rational multiple of the constant <math>e^2/h</math>. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a [[variational method]] solution, named the [[Laughlin wavefunction]].<ref name=wen-1992>{{cite journal|last=Wen|first=Xiao-Gang|title=Theory of the edge states in fractional quantum Hall effects|journal=International Journal of Modern Physics C|year=1992|volume=6|issue=10|pages=1711–1762|url=http://dao.mit.edu/~wen/pub/edgere.pdf|access-date=14 June 2012|doi=10.1142/S0217979292000840|bibcode=1992IJMPB...6.1711W|citeseerx=10.1.1.455.2763|archive-url=https://web.archive.org/web/20050522083243/http://dao.mit.edu/%7Ewen/pub/edgere.pdf|archive-date=22 May 2005|url-status=dead}}</ref> The study of topological properties of the fractional Hall effect remains an active field of research.<ref name=":0">{{Cite book|last1=Girvin|first1=Steven M.|url=https://books.google.com/books?id=2ESIDwAAQBAJ|title=Modern Condensed Matter Physics|last2=Yang|first2=Kun|date=2019-02-28|publisher=Cambridge University Press|isbn=978-1-108-57347-4|language=en}}</ref> Decades later, the aforementioned topological band theory advanced by [[David J. Thouless]] and collaborators<ref>{{Cite journal|last1=Thouless|first1=D. J.|last2=Kohmoto|first2=M.|last3=Nightingale|first3=M. P.|last4=den Nijs|first4=M.|date=1982-08-09|title=Quantized Hall Conductance in a Two-Dimensional Periodic Potential|journal=Physical Review Letters|volume=49|issue=6|pages=405–408|doi=10.1103/PhysRevLett.49.405|bibcode=1982PhRvL..49..405T|doi-access=free}}</ref> was further expanded leading to the discovery of [[topological insulator]]s.<ref>{{Cite journal|last1=Kane|first1=C. L.|last2=Mele|first2=E. J.|date=2005-11-23|title=Quantum Spin Hall Effect in Graphene|url=https://link.aps.org/doi/10.1103/PhysRevLett.95.226801|journal=Physical Review Letters|volume=95|issue=22|pages=226801|doi=10.1103/PhysRevLett.95.226801|pmid=16384250|arxiv=cond-mat/0411737|bibcode=2005PhRvL..95v6801K|s2cid=6080059}}</ref><ref>{{Cite journal|last1=Hasan|first1=M. Z.|last2=Kane|first2=C. L.|date=2010-11-08|title=Colloquium: Topological insulators|url=https://link.aps.org/doi/10.1103/RevModPhys.82.3045|journal=Reviews of Modern Physics|volume=82|issue=4|pages=3045–3067|doi=10.1103/RevModPhys.82.3045|arxiv=1002.3895|bibcode=2010RvMP...82.3045H|s2cid=16066223}}</ref> 
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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]], La<sub>2-x</sub>Ba<sub>x</sub>CuO<sub>4</sub>,  which is superconducting at temperatures as high as 39 [[kelvin]].<ref> {{citation|author=Bednorz, J.G., Müller, K.A. |title=Possible high Tc superconductivity in the Ba−La−Cu−O system.|journal= Z. Physik B - Condensed Matter |volume=64 |pages=189–193|year=1986|issue=2 |doi=10.1007/BF01303701|bibcode=1986ZPhyB..64..189B }}</ref>   It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.<ref name="physics-world str-el">{{cite journal|last=Quintanilla|first=Jorge|author2=Hooley, Chris|title=The strong-correlations puzzle|journal=Physics World|volume=22|issue=6|pages=32|date=June 2009|url=http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|access-date=14 June 2012|url-status=dead|archive-url=https://web.archive.org/web/20120906002714/http://www.isis.stfc.ac.uk/groups/theory/research/the-strong-correlations-puzzle8120.pdf|archive-date=6 September 2012|bibcode=2009PhyW...22f..32Q|doi=10.1088/2058-7058/22/06/38}}</ref> A satisfactory theoretical description of high-temperature superconductors is still not known and the field of [[strongly correlated material]]s continues to be an active research topic.
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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 />
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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.