The Origin of Topological Insulators
Maria Wasim, Aneela Sabir, Muhammad Shafiq, Rafi Ullah Khan
On the surfaces of several insulators, unusual metallic states exist. These states are created by topological phenomena, which also make the movement of electrons over interfaces that are impervious to impurity scattering. These types of topographical insulators could open up innovative pathways for creating novel phases and particles, which might find value in spintronics and quantum computing applications.
Keywords
Topological Insulator, Physics, Graphene
Published online 12/15/2023, 14 pages
Citation: Maria Wasim, Aneela Sabir, Muhammad Shafiq, Rafi Ullah Khan, The Origin of Topological Insulators, Materials Research Foundations, Vol. 154, pp 47-60, 2024
DOI: https://doi.org/10.21741/9781644902851-3
Part of the book on Topological Insulators
References
[1] F.D.M. Haldane, Model for a quantum hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Physical Review Letters 61 (1988) 2015-2018. https://doi.org/10.1103/PhysRevLett.61.2015
[2] S. Murakami, N. Nagaosa, S.C. Zhang, Spin-hall insulator, Physical Review Letters 93 (2004) 156804. https://doi.org/10.1103/PhysRevLett.93.156804
[3] C.L. Kane, E.J. Mele, Topological order and the quantum spin hall effect, Physical Review Letters 95 (2005) 146802. https://doi.org/10.1103/PhysRevLett.95.226801
[4] B. Bernevig, T. Hughes, S.C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314 (2007) 1757-61. https://doi.org/10.1126/science.1133734
[5] M. König, Quantum spin hall insulator state in HgTe quantum wells, Science 318 (2007) 766-70. https://doi.org/10.1126/science.1148047
[6] L. Fu, C. Kane, Topological insulators in three dimensions, Physical Review Letters 98 (2007) 106803. https://doi.org/10.1103/PhysRevLett.98.106803
[7] J. Moore, L. Balents, Topological invariants of time-reversal-invariant band structures. Physical Review B 75 (2006) 121306. https://doi.org/10.1103/PhysRevB.75.121306
[8] R. Roy, Topological phases and the quantum spin Hall effect in three dimensions, Physical Review B 79 (2009) 195322. https://doi.org/10.1103/PhysRevB.79.195322
[9] Y. Ran, Y. Zhang, A. Vishwanath, One-dimensional topologically protected modes in topological insulators with lattice dislocations, Nature Physics 5 (2009) 298-303. https://doi.org/10.1038/nphys1220
[10] D. Hsieh, A topological Dirac insulator in a quantum spin Hall phase, Nature 452 (2008) 970-4. https://doi.org/10.1038/nature06843
[11] D. Hsieh, Observation of unconventional quantum spin textures in topological insulators, Science (New York, N.Y.), 2009. p. 919-22. https://doi.org/10.1126/science.1167733
[12] Y. Xia, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nature Physics 5 (2009) 398-402. https://doi.org/10.1038/nphys1274
[13] H. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nature Physics 5 (2009) 438-442. https://doi.org/10.1038/nphys1270
[14] Y.L. Chen, Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3, Science (New York, N.Y.), 2009. p. 178-81.
[15] A.C. Neto, The electronic properties of graphene, Review of Modern Physics 81 (2009) 109. https://doi.org/10.1103/RevModPhys.81.109
[16] P. Roushan, Topological surface states protected From backscattering by chiral spin texture, Nature 460 (2009) 1106-9. https://doi.org/10.1038/nature08308
[17] Z. Alpichshev, STM imaging of electronic waves on the surface of Bi2Te3: Topologically protected surface states and hexagonal warping effects, Physical Review Letters 104 (2010) 016401. https://doi.org/10.1103/PhysRevLett.104.016401
[18] T. Zhang, Experimental demonstration of topological surface states protected by time-reversal symmetry, Physical Review Letters 103 (2009) 266803. https://doi.org/10.1103/PhysRevLett.103.266803
[19] K. Nomura, M. Koshino, S. Ryu, Topological delocalization of two-dimensional massless Dirac Fermions, Physical Review Letters 99 (2007) 146806. https://doi.org/10.1103/PhysRevLett.99.146806
[20] P. Anderson, Absence of diffusion in certain random lattices, Physics Review 109 (1958) 1492-1505. https://doi.org/10.1103/PhysRev.109.1492
[21] J. Li, Topological Anderson insulator, Physical Review Letters 102 (2002) 136806. https://doi.org/10.1103/PhysRevLett.102.136806
[22] C. Groth, Theory of the topological Anderson insulator, Physical Review Letters 103 (2009) 196805. https://doi.org/10.1103/PhysRevLett.103.196805
[23] D. Hsieh, A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 (2009) 1101-5. https://doi.org/10.1038/nature08234
[24] B. Seradjeh, J. Moore, M. Franz, Exciton condensation and charge fractionalization in a topological insulator film, Physical Review Letters 103 (2009) 066402. https://doi.org/10.1103/PhysRevLett.103.066402
[25] H. Peng, Aharonov-Bohm interference in topological insulator nanribbons. Nature Materials 9 (2009) 225-9. https://doi.org/10.1038/nmat2609
[26] Y. Zhang, Crossover of three-dimensional topological insulator of Bi2Se3 to the two-dimensional limit, Nature Physics 6 (2009) 584-588. https://doi.org/10.1038/nphys1689
[27] I. Garate, M. Franz, Inverse Spin-Galvanic Effect in a Topological-Insulator/Ferromagnet Interface. 2009.
[28] F. Wilczek, Two applications of Axon electrodynamics, Physical Review Letters 58 (1987) 1799-1802. https://doi.org/10.1103/PhysRevLett.58.1799
[29] X.L. Qi, T. Hughes, S.C. Zhang, Topological field theory of time-reversal invariant insulators, Physical Review B 81 (2008) 159901.
[30] X.L. Qi, Inducing a magnetic monopole with topological surface states, Science (New York, N.Y.) 323 (2009) 1184-7. https://doi.org/10.1126/science.1167747
[31] A. Essin, J. Moore, D. Vanderbilt, Magnetoelectric polarizability and Axion electrodynamics in crystalline insulators, Physical Review Letters 102 (2009) 146805. https://doi.org/10.1103/PhysRevLett.102.146805
[32] M. Fiebig, Multiferroics: Progress and prospects. Journal Physics D: Applied Physics (2005) 38. https://doi.org/10.1088/0022-3727/38/8/R01
[33] L. Fu, C. Kane, Superconducting proximity effect and Majorana Fermions at the surface of a topological insulator. Physical Review Letters 100 (2008) 096407. https://doi.org/10.1103/PhysRevLett.100.096407
[34] R. Jackiw, P. Rossi, Zero modes of the vortex-fermion system, Nuclear Physics B 190 (1981) 681-691. https://doi.org/10.1016/0550-3213(81)90044-4
[35] F. Wilczek, Majorana returns, Nature Physics 5 (2009) 614-618. https://doi.org/10.1038/nphys1380
[36] J. Nilsson, A.R. Akhmerov, C. Beenakker, Splitting of a Cooper pair by a pair of Majorana bound states. Physical Review Letters 101 (2008) 120403. https://doi.org/10.1103/PhysRevLett.101.120403
[37] G. Collins, Computing with quantum knots, Scientific American 294 (2006) 56-63. https://doi.org/10.1038/scientificamerican0406-56
