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Condensed matter physics

Phases Phase transition QCP
States of matter Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttinger liquid Time crystal
Phase phenomena Order parameter Phase transition QCP
Electronic phases Electronic band structure Plasma Insulator Mott insulator Semiconductor Semimetal Conductor Superconductor Thermoelectric Piezoelectric Ferroelectric Topological insulator Spin gapless semiconductor
Electronic phenomena Quantum Hall effect Spin Hall effect Kondo effect
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Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.

Quantum Hall effect[edit]

Quantum spin Hall effect[edit]

Magnetic monopoles[edit]

Majorana fermions[edit]

Graphene^[a]

Axions[edit]

In 2008 Shoucheng Zhang^[b] and his colleagues showed that the equations that arise in axion physics are the same as those that describe the electromagnetic behaviour of a recently discovered class of materials known, collectively, as topological insulators.

Topological quantum computing[edit]

Spintronics[edit]

History[edit]

Albert Einstein insisted that all fundamental laws of nature could be understood in terms of geometry and symmetry.^[1] Before 1980 all states of matter could be classified by the principle of broken symmetry. The quantum Hall state provided the first example of a state that had no spontaneously broken symmetry; its behaviour depended only on topology and not a specific geometry. The quantum Hall effect earned Klaus von Klitzing the Nobel Prize in Physics for 1985.

See Also[edit]

References[edit]

Definitions[edit]

Test: a test

Notes[edit]

^ See Ghaemi & Wilczek (2012)^[2]
^ See Qi et al. (2008) for the original paper and Wilczek (2009a, 2009b), Franz (2008) and Qi & Zhang (2010) for general overview on this work.

Citations[edit]

^ Qi & Zhang 2010, p. 38.
^ Wilczek 2009b, p. 617.

Popular science articles[edit]

Brumfiel, G. (2010). "Topological insulators: Star material". Nature. 466 (7304): 310–311. doi:10.1038/466310a. ISSN 0028-0836. PMID 20631773. Archived from the original on 4 Jan 2013.

Chiao, M. (2010). "Topological insulators: A hex on protection". Nature Physics. 6 (2): 81. Bibcode:2010NatPh...6...81C. doi:10.1038/nphys1529. ISSN 1745-2473.

Collins, G. P. (2006). "Computing with Quantum Knots" (PDF). Scientific American. 294 (4): 56–63. Bibcode:2006SciAm.294d..56C. doi:10.1038/scientificamerican0406-56. PMID 16596880.

Franz, M. (2008). "High-energy physics in a new guise". Physics. 1: 36. Bibcode:2008PhyOJ...1...36F. doi:10.1103/Physics.1.36. ISSN 1943-2879.

He, K. (2015). "The Quantum Hall Effect Gets More Practical". Physics. 8: 41. Bibcode:2015PhyOJ...8...41H. doi:10.1103/Physics.8.41. ISSN 1943-2879.

Kane, C. L. (2008). "Condensed matter: An insulator with a twist" (PDF). Nature Physics. 4 (5): 348–349. Bibcode:2008NatPh...4..348K. doi:10.1038/nphys955. ISSN 1745-2473.

Kane, C. L.; Moore, J. l. (2011). "Topological insulators" (PDF). Physics World. 24 (2): 32–36. Bibcode:2011PhyW...24b..32K. doi:10.1088/2058-7058/24/02/36. ISSN 0953-8585.

Manoharan, H. C. (2010). "Topological insulators: A romance with many dimensions". Nature Nanotechnology. 5 (7): 477–479. Bibcode:2010NatNa...5..477M. doi:10.1038/nnano.2010.138. ISSN 1748-3387. PMID 20606637.

Moore, J. E. (2008). "Topological order: How spin splits the electron". Nature Physics. 4 (4): 270–271. doi:10.1038/nphys925. ISSN 1745-2473.

Moore, J. (2009). "Topological insulators: The next generation". Nature Physics. 5 (6): 378–380. Bibcode:2009NatPh...5..378M. doi:10.1038/nphys1294. ISSN 1745-2473.

Moore, J. E. (2010). "The birth of topological insulators" (PDF). Nature. 464 (7286): 194–198. Bibcode:2010Natur.464..194M. doi:10.1038/nature08916. ISSN 0028-0836. PMID 20220837.

Qi, X.-L.; Zhang, S.-C. (2010). "The quantum spin Hall effect and topological insulators" (PDF). Physics Today. 63 (1): 33–38. arXiv:1001.1602. doi:10.1063/1.3293411. ISSN 0031-9228.{{cite journal}}: CS1 maint: ref duplicates default (link)

Sarma, S. D.; Freedman, M.; Nayak, C. (2006). "Topological quantum computation" (PDF). Physics Today. 59 (7): 32–38. Bibcode:2006PhT....59g..32S. doi:10.1063/1.2337825. ISSN 0031-9228.

Wilczek, F. (2009a). "Journal club". Nature. 458 (7235): 129. Bibcode:2009Natur.458..129W. doi:10.1038/458129e. ISSN 0028-0836. PMID 19279586.

Wilczek, F. (2009b). "Majorana returns" (PDF). Nature Physics. 5 (9): 614–618. Bibcode:2009NatPh...5..614W. doi:10.1038/nphys1380. ISSN 1745-2473.

Review articles[edit]

Hasan, M. Z.; Kane, C. L. (2010). "Colloquium: Topological insulators" (PDF). Reviews of Modern Physics. 82 (4): 3045–3067. arXiv:1002.3895. Bibcode:2010RvMP...82.3045H. doi:10.1103/RevModPhys.82.3045. ISSN 0034-6861.

Nayak, C.; Simon, S. H.; Stern, A.; Freedman, M.; Das Sarma, S. (2008). "Non-Abelian anyons and topological quantum computation" (PDF). Reviews of Modern Physics. 80 (3): 1083–1159. arXiv:0707.1889. Bibcode:2008RvMP...80.1083N. doi:10.1103/RevModPhys.80.1083. ISSN 0034-6861.

Žutić, I.; Fabian, J.; Sarma, S. D. (2004). "Spintronics: Fundamentals and applications" (PDF). Reviews of Modern Physics. 76 (2): 323–410. arXiv:cond-mat/0405528. Bibcode:2004RvMP...76..323Z. doi:10.1103/RevModPhys.76.323. ISSN 0034-6861.

Academic papers[edit]

Nikolić, P. (2014). "Vortices and vortex states in Rashba spin-orbit-coupled condensates". Physical Review A. 90 (2): 023623. arXiv:1406.1198. Bibcode:2014PhRvA..90b3623N. doi:10.1103/PhysRevA.90.023623. ISSN 1050-2947.

Ghaemi, P.; Wilczek, F. (2012). "Near-zero modes in superconducting graphene" (PDF). Physica Scripta. T146: 014019. arXiv:0709.2626. Bibcode:2012PhST..146a4019G. doi:10.1088/0031-8949/2012/T146/014019. ISSN 0031-8949.</ref>

Qi, X.-L.; Hughes, T. L.; Zhang, S.-C. (2008). "Topological field theory of time-reversal invariant insulators" (PDF). Physical Review B. 78 (19): 195424. arXiv:0802.3537. Bibcode:2008PhRvB..78s5424Q. doi:10.1103/PhysRevB.78.195424. ISSN 1098-0121.

Qi, X.-L.; Li, R.; Zang, J.; Zhang, S.-C. (2009). "Inducing a Magnetic Monopole with Topological Surface States" (PDF). Science. 323 (5918): 1184–1187. arXiv:0811.1303. Bibcode:2009Sci...323.1184Q. doi:10.1126/science.1167747. ISSN 0036-8075. PMID 19179491.

Weinberg, S. (1978). "A New Light Boson?" (PDF). Physical Review Letters. 40 (4): 223–226. Bibcode:1978PhRvL..40..223W. doi:10.1103/PhysRevLett.40.223. ISSN 0031-9007. S2CID 610538.

Witten, E. (1979). "Dyons of charge eθ/2π" (PDF). Physics Letters B. 86 (3–4): 283–287. Bibcode:1979PhLB...86..283W. doi:10.1016/0370-2693(79)90838-4. ISSN 0370-2693.

Condensed matter physics

States of matter

Phase phenomena

Electrons in solids

Phenomena	Hall effect quantum Hall effect spin Hall effect quantum spin Hall effect Berry phase Aharonov–Bohm effect Josephson effect Kondo effect
Theory	Drude model free electron model nearly free electron model Bloch's theorem Fermi liquid theory electronic band structure Anderson localization BCS theory tight binding model Hubbard model density functional theory
Conduction	insulator Mott insulator semiconductor semimetal conductor superconductor topological insulator spin gapless semiconductor
Couplings	thermoelectricity piezoelectricity ferroelectricity flexoelectricity electrostriction

Magnetic phases

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