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Topological insulator

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A idealized band structure for a topological insulator. The Fermi level falls within the bulk band gap which is traversed by topologically-protected surface states.

A topological insulator is a material that behaves as an insulator in its interior or bulk while permitting the movement of charges (metallic) on its surface.

In the bulk of a topological insulator the electronic band structure resembles an ordinary band insulator, with the Fermi level falling between the conduction and valence bands. On the surface of a topological insulator there are special states that fall within the bulk energy gap and allow surface metallic conduction. Carriers in these surface states have their spin locked at a right-angle to their momentum (spin-momentum locking or topological order). At a given energy the only other available electronic states have different spin, so the "U"-turn scattering is strongly suppressed and conduction on the surface is highly metallic. These states are characterized by an index (known as Z2 topological invariants) similar to the genus in topology, and are an example of topologically ordered states.[1]

Prediction and discovery

Topologically protected edge states were predicted to occur in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride (band inversion in Hg(Cd)Te was first reported in 1986 by Pankratov and collaborators),[2][3] and were observed in 2007.[4] They were predicted[5] to occur in three dimensional bulk solids of binary compounds involving bismuth. A 3D "strong topological insulator" exists which cannot be reduced to multiple copies of the quantum spin Hall state.[6]

The first experimentally realized 3D topological insulator state (topological surface states) was discovered in bismuth antimony.[7] Shortly thereafter topologically protected surface states were also observed in pure antimony, bismuth selenide, bismuth telluride and antimony telluride using ARPES.[8] Several other material systems are now believed to exhibit topological surface states.[9] In some of these materials the Fermi level actually falls in either the conduction or valence bands due to naturally occurring defects, and must be pushed into the bulk gap by doping or gating.[10][11]

Properties and applications

The surface states of a 3D Topological insulator is a new type of 2DEG (two dimensional electron gas) where electron's spin is locked to its linear momentum.[12] The topological surface states differ from Graphene due to the locking of spin and momentum.[13] Spin momentum locking or topological order allows topological surface states to host Majorana particles if superconductivity is induced on the surface of 3D topological insulators via proximity effects.[14]

The surface states in Z2 topological insulators can be destroyed by local perturbations that break the time reversal symmetry. As a result, the gapless edge/surface states of topological insulators are also not topologically protected in the strictest sense. They can be gapped/localized by local perturbations that break the time reversal symmetry. However, true topological states (such as fractional quantum Hall states) do exist, which are stable against any local perturbations that can break any symmetries. {{citation}}: Empty citation (help)

Topological order is encoded in the existence of a gas of helical Dirac fermions. Helical Dirac fermion, which behaves like a massless relativistic particle, has been observed in a 3D topological insulator.

The Z2 topological invariants cannot be measured using traditional transport method and transport is not quantized by the Z2 invariants. An experimental method to measure Z2 topological invariants was demonstrated which provide a measure of the Z2 topological order.[15]

See also

References

  1. ^ Kane, C. L. (30. September 2005). "Z2 Topological Order and the Quantum Spin Hall Effect". Physical Review Letters. 95 (14): 146802. Bibcode:2005PhRvL..95n6802K. doi:10.1103/PhysRevLett.95.146802. {{cite journal}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  2. ^ Pankratov, O.A. (1986-09-18). "Supersymmetry in Heterojunctions: Band-inverting Contact on the Basis of Pb(1-x)Sn(x)Te and Hg(1-x)Cd(x)Te". Solid State Communications. 61 (2): 93–96. doi:10.1016/0038-1098(87)90934-3. Retrieved 2011-06-15. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  3. ^ Bernevig, B. Andrei (2006-12-15). "Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells". Science. 314 (5806): 1757–1761. doi:10.1126/science.1133734. PMID 17170299. Retrieved 2010-03-25. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  4. ^ Konig, Markus (2007-11-02). "Quantum Spin Hall Insulator State in HgTe Quantum Wells". Science. 318 (5851): 766–770. doi:10.1126/science.1148047. PMID 17885096. Retrieved 2010-03-25. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  5. ^ Fu, Liang (2007-07-02). "Topological insulators with inversion symmetry". Physical Review B. 76 (4): 045302. doi:10.1103/PhysRevB.76.045302. Retrieved 2010-03-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help) Shuichi Murakami (2007). "Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase". New Journal of Physics. 9 (9): 356–356. doi:10.1088/1367-2630/9/9/356. ISSN 1367-2630. Retrieved 2010-03-26.
  6. ^ Kane, C. L. (2011). "Topological Insulators" (PDF). Physics World. 24: 32. {{cite journal}}: Cite has empty unknown parameter: |month= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  7. ^ Hsieh, D. (2008). "A Topological Dirac insulator in a quantum spin Hall phase". Nature. 452 (9): 970–974. Bibcode:2008Natur.452..970H. doi:10.1038/nature06843. PMID 18432240. Retrieved 2010. {{cite journal}}: Check date values in: |accessdate= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  8. ^ Hasan, M.Z. (2010). "Topological Insulators". Review of Modern Physics. 82 (4): 3045. Bibcode:2010RvMP...82.3045H. doi:10.1103/RevModPhys.82.3045. Retrieved 2010-03-25. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  9. ^ Lin, Hsin (2010-07). "Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena". Nat Mater. 9 (7): 546–549. doi:10.1038/nmat2771. ISSN 1476-1122. PMID 20512153. Retrieved 2010-08-05. {{cite journal}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  10. ^ Hsieh, D. (2009). "Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3". Physical Review Letters. 103 (14): 146401. Bibcode:2009PhRvL.103n6401H. doi:10.1103/PhysRevLett.103.146401. PMID 19905585. Retrieved 2010-03-25. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  11. ^ Noh, H.-J. (2008). "Spin-orbit interaction effect in the electronic structure of Bi2Te3 observed by angle-resolved photoemission spectroscopy". EPL Europhysics Letters. 81 (5): 57006. doi:10.1209/0295-5075/81/57006. Retrieved 2010-04-25. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  12. ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1038/nature08234, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1038/nature08234 instead.
  13. ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1038/nature08234, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1038/nature08234 instead.
  14. ^ Fu, L. (2008). "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator". Phys. Rev. Lett. 100: 096407. Bibcode:2008PhRvL.100i6407F. doi:10.1103/PhysRevLett.100.096407. Retrieved 2010. {{cite journal}}: Check date values in: |accessdate= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  15. ^ Hsieh, D. (2009). "Observation of Unconventional Quantum Spin Textures in Topological Insulators". Science. 323 (5916): 919–922. doi:10.1126/science.1167733. Retrieved 2010. {{cite journal}}: Check date values in: |accessdate= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
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