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Hall Effects and Berry Phase

  • Vladimir Litvinov
Chapter

Abstract

The chapter gives basic information about the Berry phase and parameters that differentiate TI from conventional dielectrics. The integer quantum Hall and intrinsic anomalous Hall effects are discussed in relation to the topology of Hilbert space in crystals.

Keywords

Adiabatic transport and Hilbert space topology Berry phase Zak phase in crystals Quantum Hall effects Spin Hall effect Quantum spin Hall effect Topological invariants Hall conductivity and Berry phase 

References

  1. 1.
    Hasan, M.Z., Kane, C.L.: Rev. Mod. Phys. 82, 3045–3067 (2010)CrossRefGoogle Scholar
  2. 2.
    Anselm, A.: Introduction to Semiconductor Theory. Prentice Hall, Englewood Cliffs, NJ (1981)Google Scholar
  3. 3.
    Wolf, C.M., Holonyak Jr., N., Stillman, G.E.: Physical Properties of Semiconductors. Prentice Hall, Englewood Cliffs, NJ (1989)Google Scholar
  4. 4.
    Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A.H., Ong, N.P.: Rev. Mod. Phys. 82, 1539–1592 (2010)CrossRefGoogle Scholar
  5. 5.
    Dyakonov, M.I.: Proc. SPIE. 7036, R1–R14 (2008)Google Scholar
  6. 6.
    Karplus, R., Luttinger, J.M.: Phys. Rev. 95, 1154 (1954)CrossRefGoogle Scholar
  7. 7.
    Dyakonov, M.I., Perel, V.I.: JETP Lett. 13, 467–469 (1971)Google Scholar
  8. 8.
    Kato, Y.K., Myers, R.C., Gossard, A.C., Awschalom, D.D.: Science. 306, 1910 (2004)CrossRefGoogle Scholar
  9. 9.
    Wunderlich, J., Kaestner, B., Sinova, J., Jungwirth, T.: Phys. Rev. Lett. 94, 047204 (2005)CrossRefGoogle Scholar
  10. 10.
    Valenzuela, S.O., Tinkham, M.: Nature. 442, 176 (2006)CrossRefGoogle Scholar
  11. 11.
    Sinova, J., Valenzuela, S.O., Wunderlich, J., Back, C.H., Jungwirth, T.: Rev. Mod. Phys. 87, 1213 (2015)CrossRefGoogle Scholar
  12. 12.
    Berry, M.V.: Proc. R. Soc. Lond. A392, 45 (1984)CrossRefGoogle Scholar
  13. 13.
    Sakurai, J.J.: Modern Quantum Mechanics. Addison Wesley, Reading, MA (1993)Google Scholar
  14. 14.
    Chern, S.S.: Ann. Math. 46, 674–684 (1945)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nakahara, M.: Geometry, Topology and Physics. Taylor and Francis, New York & London (2003)zbMATHGoogle Scholar
  16. 16.
    Hatsugai, Y.: J. Physical Soc. Japan. 75, 123601 (2006)CrossRefGoogle Scholar
  17. 17.
    Zak, J.: Phys. Rev. Lett. 62, 27472750 (1989)CrossRefGoogle Scholar
  18. 18.
    Resta, R.: J. Phys. Condens. Matter. 12, R107–R143 (2000)CrossRefGoogle Scholar
  19. 19.
    Sundaram, G., Niu, Q.: Phys. Rev. B59, 14915 (1999)CrossRefGoogle Scholar
  20. 20.
    Xiao, D., Chang, M.C., Niu, Q.: Rev. Mod. Phys. 82, 1959–2007 (2010)CrossRefGoogle Scholar
  21. 21.
    “Berry’s Phase and Geometric Quantum Distance: Macroscopic Polarization and Electron Localization”. https://cds.cern.ch/record/893386, EPFL, Lausanne (2000)
  22. 22.
    Adams, E.N., Blount, E.I.: J. Phys. Chem. Solid. 10, 286 (1959)CrossRefGoogle Scholar
  23. 23.
    Blount, E.I.: In: Seitz, F., Turnbull, D. (eds.) Solid State Physics, vol. 13, p. 305. Academic Press, New York (1962)Google Scholar
  24. 24.
    Marder, M.: Condensed Matter Physics. Wiley, New York (2000)Google Scholar
  25. 25.
    Shindou, R., Imura, K.: Nucl. Phys. B720, 399–435 (2005)CrossRefGoogle Scholar
  26. 26.
    Onoda, M., Nagaosa, N.: J. Phys. Soc. Japan. 71(1), 19–22 (2002)CrossRefGoogle Scholar
  27. 27.
    Sinova, J., Culcer, D., Nui, Q., Sinitsyn, N.A., Jungwirth, T., MacDonald, A.H.: Phys. Rev. Lett. 92(12), 126603 (2004)CrossRefGoogle Scholar
  28. 28.
    Yao, Y., Fang, Z.: Phys. Rev. Lett. 95, 156601 (2005)CrossRefGoogle Scholar
  29. 29.
    von Klitzing, K., Dorda, G., Pepper, M.: Phys. Rev. Lett. 45, 494 (1980)CrossRefGoogle Scholar
  30. 30.
    Weng, H., Yu, R., Hu, X., Dai, X., Fang, Z.: arXiv:1508.02967v3 [cond-mat.mes-hall] (2015)Google Scholar
  31. 31.
    Thouless, J.D., Kohmoto, M., Nightingale, P., den Nijs, M.: Phys. Rev. Lett. 49, 405 (1982)CrossRefGoogle Scholar
  32. 32.
    Ando, Y.: J. Phys. Soc. Jpn. 82, 102001 (2013)CrossRefGoogle Scholar
  33. 33.
    Laughlin, R.B.: Phys. Rev. B23, 5632 (1981)CrossRefGoogle Scholar
  34. 34.
    Halperin, B.I.: Phys. Rev. B25, 2185 (1982)CrossRefGoogle Scholar
  35. 35.
    Haldane, F.D.M.: Phys. Rev. Lett. 61, 2015 (1988)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Jain, J.K.: Adv. Phys. 41, 105 (1992)CrossRefGoogle Scholar
  37. 37.
    Liu, C.X., Qi, X.L., Dai, X., Fang, Z., Zhang, S.C.: Phys. Rev. Lett. 101, 146802 (2008)CrossRefGoogle Scholar
  38. 38.
    Yu, R., Zhang, W., Zhang, H.J., Zhang, S.C., Dai, X., Fang, Z.: Science. 329, 61 (2010)CrossRefGoogle Scholar
  39. 39.
    Chang, C.Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., Ou, Y., Wei, P., Wang, L.L., Ji, Z.Q., Feng, Y., Ji, S., Chen, X., Jia, J., Dai, X., Fang, Z., Zhang, S.C., He, K., Wang, Y., Lu, L., Ma, X.C., Xue, Q.K.: Science. 340, 167–170 (2013)CrossRefGoogle Scholar
  40. 40.
    Checkelsky, J.G., Yoshimi, R., Tsukazaki, A., Tahakashi, K.S., Kozuka, Y., Falson, J., Kawasaki, M., Tokura, Y.: Nat. Phys. 10, 731–736 (2014)CrossRefGoogle Scholar
  41. 41.
    Kou, X., Guo, S.T., Fan, Y., Pan, L., Lang, M., Jiang, Y., Shao, Q., Nie, T., Murata, K., Tang, J., Wang, Y., He, L., Lee, T.K., Lee, W.L., Wang, K.L.: Phys. Rev. Lett. 113, 137201 (2014)CrossRefGoogle Scholar
  42. 42.
    Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 146802 (2005)CrossRefGoogle Scholar
  43. 43.
    Bernevig, B.A., Zhang, S.C.: Phys. Rev. Lett. 96, 106802 (2006)CrossRefGoogle Scholar
  44. 44.
    Bernevig, B.A., Hughes, T.L., Zhang, S.C.: Science. 314, 1757 (2006)CrossRefGoogle Scholar
  45. 45.
    Konig, M., Wiedmann, S., Brüne, C., Roth, A, Buhmann, H., Molenkamp, L.W., Qi, X.-L., Zhang, S.-C.: Science. 318, 766 (2006)CrossRefGoogle Scholar
  46. 46.
    Roth, A., Brüne, C., Buhmann, H., Molenkamp, L.W., Maciejko, J., Qi, X.-L., Zhang, S.-C.: Science. 325, 294 (2009)CrossRefGoogle Scholar
  47. 47.
    Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 226801 (2005)CrossRefGoogle Scholar
  48. 48.
    Wang, J., Lian, B., Zhang, H., Zhang, S.C.: Phys. Rev. Lett. 111, 086803 (2013)CrossRefGoogle Scholar
  49. 49.
    Wang, J., Lian, B., Zhang, S.C.: arXiv:1409.6715v4 [cond-mat.mes-hall] (2015)Google Scholar
  50. 50.
    Fu, L., Kane, C.L.: Phys. Rev. B76, 045302 (2007)CrossRefGoogle Scholar
  51. 51.
    Fruchart, M., Carpentier, D.: arXiv:1310.0255v2 [cond-mat.mes-hall] (2013)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vladimir Litvinov
    • 1
  1. 1.Sierra Nevada CorporationIrvineUSA

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