Skip to main content
SpringerLink
Log in
Book cover

Magnetism in Topological Insulators pp 25–53Cite as

Hall Effects and Berry Phase

  • Chapter
  • First Online:

  • 1041 Accesses

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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Hasan, M.Z., Kane, C.L.: Rev. Mod. Phys. 82, 3045–3067 (2010)

    Google Scholar 

  2. Anselm, A.: Introduction to Semiconductor Theory. Prentice Hall, Englewood Cliffs, NJ (1981)

    Google Scholar 

  3. Wolf, C.M., Holonyak Jr., N., Stillman, G.E.: Physical Properties of Semiconductors. Prentice Hall, Englewood Cliffs, NJ (1989)

    Google Scholar 

  4. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A.H., Ong, N.P.: Rev. Mod. Phys. 82, 1539–1592 (2010)

    Google Scholar 

  5. Dyakonov, M.I.: Proc. SPIE. 7036, R1–R14 (2008)

    Google Scholar 

  6. Karplus, R., Luttinger, J.M.: Phys. Rev. 95, 1154 (1954)

    Google Scholar 

  7. Dyakonov, M.I., Perel, V.I.: JETP Lett. 13, 467–469 (1971)

    Google Scholar 

  8. Kato, Y.K., Myers, R.C., Gossard, A.C., Awschalom, D.D.: Science. 306, 1910 (2004)

    Google Scholar 

  9. Wunderlich, J., Kaestner, B., Sinova, J., Jungwirth, T.: Phys. Rev. Lett. 94, 047204 (2005)

    Google Scholar 

  10. Valenzuela, S.O., Tinkham, M.: Nature. 442, 176 (2006)

    Google Scholar 

  11. Sinova, J., Valenzuela, S.O., Wunderlich, J., Back, C.H., Jungwirth, T.: Rev. Mod. Phys. 87, 1213 (2015)

    Google Scholar 

  12. Berry, M.V.: Proc. R. Soc. Lond. A392, 45 (1984)

    Google Scholar 

  13. Sakurai, J.J.: Modern Quantum Mechanics. Addison Wesley, Reading, MA (1993)

    Google Scholar 

  14. Chern, S.S.: Ann. Math. 46, 674–684 (1945)

    MathSciNet  Google Scholar 

  15. Nakahara, M.: Geometry, Topology and Physics. Taylor and Francis, New York & London (2003)

    MATH  Google Scholar 

  16. Hatsugai, Y.: J. Physical Soc. Japan. 75, 123601 (2006)

    Google Scholar 

  17. Zak, J.: Phys. Rev. Lett. 62, 27472750 (1989)

    Google Scholar 

  18. Resta, R.: J. Phys. Condens. Matter. 12, R107–R143 (2000)

    Google Scholar 

  19. Sundaram, G., Niu, Q.: Phys. Rev. B59, 14915 (1999)

    Google Scholar 

  20. Xiao, D., Chang, M.C., Niu, Q.: Rev. Mod. Phys. 82, 1959–2007 (2010)

    Google Scholar 

  21. “Berry’s Phase and Geometric Quantum Distance: Macroscopic Polarization and Electron Localization”. https://cds.cern.ch/record/893386, EPFL, Lausanne (2000)

  22. Adams, E.N., Blount, E.I.: J. Phys. Chem. Solid. 10, 286 (1959)

    Google Scholar 

  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. Marder, M.: Condensed Matter Physics. Wiley, New York (2000)

    Google Scholar 

  25. Shindou, R., Imura, K.: Nucl. Phys. B720, 399–435 (2005)

    Google Scholar 

  26. Onoda, M., Nagaosa, N.: J. Phys. Soc. Japan. 71(1), 19–22 (2002)

    Google Scholar 

  27. Sinova, J., Culcer, D., Nui, Q., Sinitsyn, N.A., Jungwirth, T., MacDonald, A.H.: Phys. Rev. Lett. 92(12), 126603 (2004)

    Google Scholar 

  28. Yao, Y., Fang, Z.: Phys. Rev. Lett. 95, 156601 (2005)

    Google Scholar 

  29. von Klitzing, K., Dorda, G., Pepper, M.: Phys. Rev. Lett. 45, 494 (1980)

    Google Scholar 

  30. Weng, H., Yu, R., Hu, X., Dai, X., Fang, Z.: arXiv:1508.02967v3 [cond-mat.mes-hall] (2015)

    Google Scholar 

  31. Thouless, J.D., Kohmoto, M., Nightingale, P., den Nijs, M.: Phys. Rev. Lett. 49, 405 (1982)

    Google Scholar 

  32. Ando, Y.: J. Phys. Soc. Jpn. 82, 102001 (2013)

    Google Scholar 

  33. Laughlin, R.B.: Phys. Rev. B23, 5632 (1981)

    Google Scholar 

  34. Halperin, B.I.: Phys. Rev. B25, 2185 (1982)

    Google Scholar 

  35. Haldane, F.D.M.: Phys. Rev. Lett. 61, 2015 (1988)

    MathSciNet  Google Scholar 

  36. Jain, J.K.: Adv. Phys. 41, 105 (1992)

    Google Scholar 

  37. Liu, C.X., Qi, X.L., Dai, X., Fang, Z., Zhang, S.C.: Phys. Rev. Lett. 101, 146802 (2008)

    Google Scholar 

  38. Yu, R., Zhang, W., Zhang, H.J., Zhang, S.C., Dai, X., Fang, Z.: Science. 329, 61 (2010)

    Google Scholar 

  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)

    Google Scholar 

  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)

    Google Scholar 

  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)

    Google Scholar 

  42. Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 146802 (2005)

    Google Scholar 

  43. Bernevig, B.A., Zhang, S.C.: Phys. Rev. Lett. 96, 106802 (2006)

    Google Scholar 

  44. Bernevig, B.A., Hughes, T.L., Zhang, S.C.: Science. 314, 1757 (2006)

    Google Scholar 

  45. Konig, M., Wiedmann, S., Brüne, C., Roth, A, Buhmann, H., Molenkamp, L.W., Qi, X.-L., Zhang, S.-C.: Science. 318, 766 (2006)

    Google Scholar 

  46. Roth, A., Brüne, C., Buhmann, H., Molenkamp, L.W., Maciejko, J., Qi, X.-L., Zhang, S.-C.: Science. 325, 294 (2009)

    Google Scholar 

  47. Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 226801 (2005)

    Google Scholar 

  48. Wang, J., Lian, B., Zhang, H., Zhang, S.C.: Phys. Rev. Lett. 111, 086803 (2013)

    Google Scholar 

  49. Wang, J., Lian, B., Zhang, S.C.: arXiv:1409.6715v4 [cond-mat.mes-hall] (2015)

    Google Scholar 

  50. Fu, L., Kane, C.L.: Phys. Rev. B76, 045302 (2007)

    Google Scholar 

  51. Fruchart, M., Carpentier, D.: arXiv:1310.0255v2 [cond-mat.mes-hall] (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sierra Nevada Corporation, Irvine, CA, USA

    Vladimir Litvinov

Authors
  1. Vladimir Litvinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Litvinov, V. (2020). Hall Effects and Berry Phase. In: Magnetism in Topological Insulators. Springer, Cham. https://doi.org/10.1007/978-3-030-12053-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-12053-5_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12052-8

  • Online ISBN: 978-3-030-12053-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation