, Volume 52, Issue 14, pp 1868–1870 | Cite as

On Derivation of Dresselhaus Spin-Splitting Hamiltonians in One-Dimensional Electron Systems

  • I. A. KokurinEmail author


Two-dimensional (2D) semiconductor structures of materials without inversion center (e.g. zinc-blende AIIIBV) possess the zero-field conduction band spin-splitting (Dresselhaus term), which is linear and cubic in wavevector k, that arises from cubic in k splitting in bulk material. At low carrier concentration the cubic term is usually negligible. However, if we will be interested in the following dimensional quantization (in 2D plane) and the character width in this direction is comparable with the width of 2D-structure, then we have to take into account k3-terms as well (even at low concentrations), that after quantization leads to comparable contribution that arises from k-linear term. We propose the general procedure for derivation of Dresselhaus spin-splitting Hamiltonian applicable for any curvilinear 1D-structures. The simple examples for the cases of quantum wire (QWr) and quantum ring (QR) defined in usual [001]-grown 2D-structure are presented.


  1. 1.
    M. I. Dyakonov and V. I. Perel, Sov. Phys. Solid State 13, 3023 (1972).Google Scholar
  2. 2.
    M. I. Dyakonov and V. Yu. Kachorovskii, Sov. Phys. Semicond. 20, 110 (1986).Google Scholar
  3. 3.
    E. L. Ivchenko and S. D. Ganichev, in Spin Physics in Semiconductors, Ed. by M. I. Dyakonov (Berlin, Springer, 2008), p. 245.Google Scholar
  4. 4.
    N. S. Averkiev and I. A. Kokurin, J. Magn. Magn. Mater. 440, 157 (2017).ADSCrossRefGoogle Scholar
  5. 5.
    J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    Yu. A. Bychkov and E. I. Rashba, JETP Lett. 39, 78 (1984).ADSGoogle Scholar
  7. 7.
    G. Dresselhaus, Phys. Rev. 100, 580 (1955).ADSCrossRefGoogle Scholar
  8. 8.
    U. Rössler and J. Keinz, Solid State Commun. 121, 313 (2002).ADSCrossRefGoogle Scholar
  9. 9.
    E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures. Symmetry and Optical Phenomena (Berlin, Springer, 1997).CrossRefzbMATHGoogle Scholar
  10. 10.
    I. A. Kokurin, Physica E (Amsterdam) 74, 264 (2015).Google Scholar
  11. 11.
    J. S. Sheng and K. Chang, Phys. Rev. B 74, 235315 (2006).ADSCrossRefGoogle Scholar
  12. 12.
    I. A. Kokurin, Semiconductors 52, 535 (2018).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Physics and Chemistry, Mordovia State UniversitySaranskRussia
  2. 2.Ioffe InstituteSt. PetersburgRussia
  3. 3.St. Petersburg Electrotechnical University “LETI”St. PetersburgRussia

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