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]

Contents

[edit] 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]

[edit] 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. 

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]

[edit] References

  1. ^ Kane, C. L.; Mele, E. J. (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. http://link.aps.org/doi/10.1103/PhysRevLett.95.146802. 
  2. ^ Pankratov, O.A.; S.V. Pakhomov, B.A. Volkov (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. http://www.sciencedirect.com/science/article/pii/0038109887909343. Retrieved 2011-06-15. 
  3. ^ Bernevig, B. Andrei; Taylor L. Hughes, Shou-Cheng Zhang (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. http://www.sciencemag.org/cgi/content/abstract/314/5806/1757. Retrieved 2010-03-25. 
  4. ^ Konig, Markus; Steffen Wiedmann, Christoph Brune, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, Shou-Cheng Zhang (2007-11-02). "Quantum Spin Hall Insulator State in HgTe Quantum Wells". Science 318 (5851): 766–770. doi:10.1126/science.1148047. PMID 17885096. http://www.sciencemag.org/cgi/content/abstract/318/5851/766. Retrieved 2010-03-25. 
  5. ^ Fu, Liang; C. L. Kane (2007-07-02). "Topological insulators with inversion symmetry". Physical Review B 76 (4): 045302. doi:10.1103/PhysRevB.76.045302. http://link.aps.org/doi/10.1103/PhysRevB.76.045302. Retrieved 2010-03-26.  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. http://iopscience.iop.org/1367-2630/9/9/356/. Retrieved 2010-03-26. 
  6. ^ Kane, C. L.; Moore, J. E. (2011). "Topological Insulators". Physics World 24: 32. http://www.physics.upenn.edu/~kane/pubs/p69.pdf. 
  7. ^ Hsieh, D.; D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava & M. Z. Hasan (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. http://www.nature.com/nature/journal/v452/n7190/full/nature06843.html. Retrieved 2010. 
  8. ^ Hasan, M.Z.; Kane, C.L. (2010). "Topological Insulators". Review of Modern Physics 82 (4): 3045. Bibcode 2010RvMP...82.3045H. doi:10.1103/RevModPhys.82.3045. http://link.aps.org/doi/10.1103/RevModPhys.82.3045. Retrieved 2010-03-25. 
  9. ^ Lin, Hsin; L. Andrew Wray, Yuqi Xia, Suyang Xu, Shuang Jia, Robert J. Cava, Arun Bansil, M. Zahid Hasan (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. http://dx.doi.org.proxy.library.cornell.edu/10.1038/nmat2771. Retrieved 2010-08-05. 
  10. ^ Hsieh, D.; Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, M. Z. Hasan (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. http://link.aps.org/doi/10.1103/PhysRevLett.103.146401. Retrieved 2010-03-25. 
  11. ^ Noh, H.-J.; H. Koh, S.-J. Oh, J.-H. Park, H.-D. Kim, J. D. Rameau, T. Valla, T. E. Kidd, P. D. Johnson, Y. Hu and Q. Li (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. http://iopscience.iop.org/0295-5075/81/5/57006/. Retrieved 2010-04-25. 
  12. ^ Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Dil, J.; Meier, F.; Osterwalder, J.; Patthey, L. et al (2009). "A tunable topological insulator in the spin helical Dirac transport regime". Nature 460 (7259): 1101–1105. Bibcode 2009Natur.460.1101H. doi:10.1038/nature08234. PMID 19620959.  edit
  13. ^ Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Dil, J.; Meier, F.; Osterwalder, J.; Patthey, L. et al (2009). "A tunable topological insulator in the spin helical Dirac transport regime". Nature 460 (7259): 1101–1105. Bibcode 2009Natur.460.1101H. doi:10.1038/nature08234. PMID 19620959.  edit
  14. ^ Fu, L.; C. L. Kane (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. http://link.aps.org/doi/10.1103/PhysRevLett.100.096407. Retrieved 2010. 
  15. ^ Hsieh, D.; D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, F. Meier, J. Osterwalder, C. L. Kane, G. Bihlmayer, Y. S. Hor, R. J. Cava and M. Z. Hasan (2009). "Observation of Unconventional Quantum Spin Textures in Topological Insulators". Science 323 (5916): 919–922. doi:10.1126/science.1167733. http://www.sciencemag.org/content/323/5916/919.full. Retrieved 2010. 

[edit] Further reading

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