Editing Condensed matter physics (section)

==History==
{{Further|Timeline of condensed matter physics}}

===Classical physics===
[[File:Heike Kamerlingh Onnes and Johannes Diderik van der Waals.jpg|thumb|upright|[[Heike Kamerlingh Onnes]] and [[Johannes van der Waals]] with the [[helium]] ''liquefactor'' at Leiden in 1908]]

One of the first studies of condensed states of matter was by [[People of England|English]] [[chemist]] [[Humphry Davy]], in the first decades of the nineteenth century. Davy observed that of the forty [[chemical element]]s known at the time, twenty-six had [[metal]]lic properties such as [[lustre (mineralogy)|lustre]], [[ductility]] and high electrical and thermal conductivity.<ref name=goodstein>{{cite journal|last1=Goodstein|first1=David|author1-link=David Goodstein|last2=Goodstein|first2=Judith|author2-link=Judith R. Goodstein|title=Richard Feynman and the History of Superconductivity|journal=Physics in Perspective|year=2000|volume=2|issue=1|url=http://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|access-date=7 April 2012|doi=10.1007/s000160050035|pages=30|bibcode=2000PhP.....2...30G|s2cid=118288008|archive-url=https://web.archive.org/web/20151117113759/https://web.njit.edu/~tyson/supercon_papers/Feynman_Superconductivity_History.pdf|archive-date=17 November 2015|url-status=dead}}</ref> This indicated that the atoms in [[John Dalton]]'s [[atomic theory]] were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as [[nitrogen]] and [[hydrogen]] could be liquefied under the right conditions and would then behave as metals.<ref name=davy-1839>{{cite book |editor-last=Davy |editor-first = John |title=The collected works of Sir Humphry Davy: Vol. II |year=1839|publisher=Smith Elder & Co., Cornhill |url = https://archive.org/details/bub_gb_6WNKAAAAYAAJ |page=[https://archive.org/details/bub_gb_6WNKAAAAYAAJ/page/n34 22] }}</ref>{{NoteTag|Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists [[Eugene Wigner]] and [[Hillard Bell Huntington]] predicted in 1935<ref name=metallic-hydrogen>{{cite journal |last=Silvera|first=Isaac F.|author2=Cole, John W. |title=Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist|journal=Journal of Physics|year=2010|volume=215|issue=1 |doi=10.1088/1742-6596/215/1/012194 |bibcode= 2010JPhCS.215a2194S |pages=012194 |url = http://nrs.harvard.edu/urn-3:HUL.InstRepos:9569212 |doi-access=free}}</ref> that a state [[metallic hydrogen]] exists at sufficiently high pressures (over 25 [[Pascal (unit)|GPa]]), but this has not yet been observed.}}

In 1823, [[Michael Faraday]], then an assistant in Davy's lab, successfully liquefied [[chlorine]] and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and [[oxygen]].<ref name=goodstein /> Shortly after, in 1869, [[People of Ireland|Irish]] chemist [[Thomas Andrews (scientist)|Thomas Andrews]] studied the [[phase transition]] from a liquid to a gas and coined the term [[Critical point (thermodynamics)|critical point]] to describe the condition where a gas and a liquid were indistinguishable as phases,<ref name=thomasandrews>{{cite journal|last=Rowlinson|first=J. S.|title=Thomas Andrews and the Critical Point|journal=Nature|year=1969|volume=224|issue=8|doi=10.1038/224541a0|pages=541–543|bibcode= 1969Natur.224..541R|s2cid=4168392}}</ref> and [[Netherlands|Dutch]] physicist [[Johannes van der Waals]] supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.<ref name=atkins>{{cite book|last1=Atkins|first1=Peter|last2=de Paula|first2=Julio|title=Elements of Physical Chemistry|year=2009|publisher=Oxford University Press|isbn=978-1-4292-1813-9}}</ref>{{rp|35–38}} By 1908, [[James Dewar]] and [[Heike Kamerlingh Onnes]] were successfully able to liquefy hydrogen and the then newly discovered [[helium]] respectively.<ref name=goodstein />

[[Paul Drude]] in 1900 proposed the first theoretical model for a classical [[electron]] moving through a metallic solid.<ref name=marvincohen2008 /> Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as the [[Wiedemann–Franz law]].<ref name="Kittel 1996">{{cite book|last=Kittel|first=Charles|title=[[Introduction to Solid State Physics]]|year=1996|publisher=John Wiley & Sons|isbn=978-0-471-11181-8}}</ref><ref name=Hoddeson-1992>{{cite book|last=Hoddeson|first=Lillian|title=Out of the Crystal Maze: Chapters from The History of Solid State Physics|year=1992|publisher=Oxford University Press|isbn=978-0-19-505329-6|url=https://books.google.com/books?id=WCpPPHhMdRcC&pg=PA29}}</ref>{{rp|27–29}} However, despite the success of [[Drude model|Drude's model]], it had one notable problem: it was unable to correctly explain the electronic contribution to the [[specific heat]] and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.<ref name=Kragh2002>{{cite book |last= Kragh |first= Helge |title= Quantum Generations: A History of Physics in the Twentieth Century |publisher= Princeton University Press |edition= Reprint |date= 2002 |isbn= 978-0-691-09552-3}}</ref>{{rp|366–368}}

In 1911, three years after helium was first liquefied, Onnes working at [[University of Leiden]] discovered [[superconductivity]] in [[mercury (element)|mercury]], when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.<ref name=vanDelft2010>{{cite journal|last=van Delft|first=Dirk|author2=Kes, Peter |title=The discovery of superconductivity|journal=Physics Today|date=September 2010|volume=63|issue=9|doi=10.1063/1.3490499|url=http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.lorentz.leidenuniv.nl/history/cold/DelftKes_HKO_PT.pdf |archive-date=2022-10-09 |url-status=live|access-date=7 April 2012|bibcode= 2010PhT....63i..38V|pages=38–43|doi-access=free}}</ref> The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.<ref name=Slichter-AIP-supercond>{{cite web|last=Slichter|first=Charles|title=Introduction to the History of Superconductivity|url=http://www.aip.org/history/mod/superconductivity/01.html|website=Moments of Discovery|publisher=American Institute of Physics|access-date=13 June 2012|archive-url=https://web.archive.org/web/20120515123519/http://www.aip.org/history/mod/superconductivity/01.html|archive-date=15 May 2012|url-status=dead}}</ref> [[Albert Einstein]], in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."<ref name=Schmalian-2010>{{cite journal|last=Schmalian|first=Joerg|title=Failed theories of superconductivity|year=2010|arxiv=1008.0447|bibcode= 2010MPLB...24.2679S |doi= 10.1142/S0217984910025280|journal=Modern Physics Letters B|volume=24|issue=27|pages=2679–2691|s2cid=119220454}}</ref>

===Advent of quantum mechanics===
Drude's classical model was augmented by [[Wolfgang Pauli]], [[Arnold Sommerfeld]], [[Felix Bloch]] and other physicists.  Pauli realized that the free electrons in metal must obey the [[Fermi–Dirac statistics]].  Using this idea, he developed the theory of [[paramagnetism]] in 1926.  Shortly after, Sommerfeld incorporated the [[Fermi–Dirac statistics]] into the [[free electron model]] and made it better to explain the heat capacity.  Two years later, Bloch used [[quantum mechanics]] to describe the motion of an electron in a periodic lattice.<ref name=Kragh2002/>{{rp|366–368}}

The mathematics of crystal structures developed by [[Auguste Bravais]], [[Yevgraf Fyodorov]] and others was used to classify crystals by their [[symmetry group]], and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935.<ref name=Aroyo-2006>{{Cite book|last=Aroyo|first=Mois, I.|author2=Müller, Ulrich|author3=Wondratschek, Hans|title=Historical introduction|year=2006|volume=A|pages=2–5|doi=10.1107/97809553602060000537|series=International Tables for Crystallography|isbn=978-1-4020-2355-2|url=http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|citeseerx=10.1.1.471.4170|access-date=2017-10-24|archive-date=2008-10-03|archive-url=https://web.archive.org/web/20081003122816/http://www.european-arachnology.org/proceedings/19th/Lourenco.PDF|url-status=dead}}</ref> [[Band theory|Band structure calculations]] were first used in 1930 to predict the properties of new materials, and in 1947 [[John Bardeen]], [[Walter Brattain]] and [[William Shockley]] developed the first [[semiconductor]]-based [[transistor]], heralding a revolution in electronics.<ref name=marvincohen2008 />

[[File:Replica-of-first-transistor.jpg|thumb|left|A replica of the first [[point-contact transistor]] in [[Bell labs]]]]
In 1879, [[Edwin Herbert Hall]] working at the [[Johns Hopkins University]] discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.<ref>{{cite journal|title=On a New Action of the Magnet on Electric Currents|author=Hall, Edwin|journal=American Journal of Mathematics|volume=2|year=1879|pages=287–92|url=http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|access-date=2008-02-28|doi=10.2307/2369245|issue=3|jstor=2369245|s2cid=107500183 |url-status=dead|archive-url=https://web.archive.org/web/20070208040346/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|archive-date=2007-02-08}}</ref> This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the [[Hall effect]], but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, [[Lev Landau]] in 1930 developed the theory of [[Landau quantization]] and laid the foundation for a theoretical explanation of the [[quantum Hall effect]] which was discovered half a century later.<ref>{{cite book|first1=L. D.|last1=Landau|first2=E. M.|last2=Lifshitz|title=Quantum Mechanics: Nonrelativistic Theory|year=1977|publisher=Pergamon Press|isbn=978-0-7506-3539-4}}</ref>{{rp|458–460}}<ref>{{cite journal|title=Focus: Landmarks—Accidental Discovery Leads to Calibration Standard|date=2015-05-15|first=David|last=Lindley|journal=Physics|volume=8|page=46 |doi=10.1103/Physics.8.46}}</ref>

Magnetism as a property of matter has been known in China since 4000 BC.<ref name=mattis-magnetism-2006>{{cite book|last=Mattis|first=Daniel|title=The Theory of Magnetism Made Simple|year=2006|publisher=World Scientific|isbn=978-981-238-671-7}}</ref>{{rp|1–2}} However, the first modern studies of magnetism only started with the development of [[electrodynamics]] by Faraday, [[James Clerk Maxwell|Maxwell]] and others in the nineteenth century, which included classifying materials as [[ferromagnetic]], [[paramagnetic]] and [[diamagnetic]] based on their response to magnetization.<ref name=Chatterjee-2004-ferromagnetism>{{cite journal|last=Chatterjee|first=Sabyasachi|title=Heisenberg and Ferromagnetism|journal=Resonance|date=August 2004|volume=9|issue=8|doi=10.1007/BF02837578|url=http://www.ias.ac.in/describe/article/reso/009/08/0057-0066|access-date=13 June 2012|pages=57–66|s2cid=123099296}}</ref> [[Pierre Curie]] studied the dependence of magnetization on temperature and discovered the [[Curie point]] phase transition in ferromagnetic materials.<ref name=mattis-magnetism-2006 /> In 1906, [[Pierre Weiss]] introduced the concept of [[magnetic domain]]s to explain the main properties of ferromagnets.<ref name=Visintin-domains>{{cite book|last=Visintin|first=Augusto|title=Differential Models of Hysteresis|year=1994|publisher=Springer|isbn=978-3-540-54793-8|url=https://books.google.com/books?id=xZrTIDmNOlgC&pg=PA9}}</ref>{{rp|9}} The first attempt at a microscopic description of magnetism was by [[Wilhelm Lenz]] and [[Ernst Ising]] through the [[Ising model]] that described magnetic materials as consisting of a periodic lattice of [[Spin (physics)|spins]] that collectively acquired magnetization.<ref name=mattis-magnetism-2006/> The Ising model was solved exactly to show that [[spontaneous magnetization]] can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch on [[spin wave]]s and [[Néel]] on [[antiferromagnetism]] led to developing new magnetic materials with applications to [[magnetic storage]] devices.<ref name=mattis-magnetism-2006/>{{rp|36–38,g48}}

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