Physics of the Solid State

, Volume 61, Issue 11, pp 2090–2095 | Cite as

Effect of Nonequilibrium Correlations on the Effective Resistances between Sites in the Theory of Hopping Conductivity

  • A. V. ShumilinEmail author
  • Y. M. Beltukov


It has been shown that the nonequilibrium correlations in hopping conductivity can be taken into account by generalizing the Miller–Abrahams network of resistors. The resistances of resistors between nodes in such a network are related to their environment. Moreover, some nonlocal elements exist, which create the voltage on one resistor proportional to the current through the other resistor. These elements are required to make controllable the approximation used to construct the network. The greatest change in the resistance takes place in the resistors, whose resistance is lower than the critical resistance of the percolation theory.


hopping conductivity correlation of occupation numbers Miller–Abrahams network of resistors 



The authors declare that they have no conflicts of interest.


  1. 1.
    A. Miller and E. Abrahams, Phys. Rev. 120, 745 (1960).ADSCrossRefGoogle Scholar
  2. 2.
    B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer, Berlin, 1984).CrossRefGoogle Scholar
  3. 3.
    P. M. Richards, Phys. Rev. B 16, 1393 (1977).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    E. I. Levin, V. L. Nguen, and B. I. Shklovskii, Sov. Phys. JETP 55, 921 (1982).Google Scholar
  5. 5.
    O. Mermer, G. Veeraraghavan, T. L. Francis, Y. Sheng, D. T. Nguyen, M. Wohlgenannt, A. Kohler, M. K. Al-Suti, and M. S. Khan, Phys. Rev. B 72, 205202 (2005).ADSCrossRefGoogle Scholar
  6. 6.
    A. V. Shumilin and V. V. Kabanov, Phys. Rev. B 92, 014206 (2015).ADSCrossRefGoogle Scholar
  7. 7.
    A. V. Shumilin, V. V. Kabanov, and V. I. Dedieu, Phys. Rev. B 97, 094201 (2018).ADSCrossRefGoogle Scholar
  8. 8.
    K. S. Chase and D. J. Thouless, Phys. Rev. B 39, 9809 (1989).ADSCrossRefGoogle Scholar
  9. 9.
    O. Agam and I. L. Aleiner, Phys. Rev. B 89, 224204 (2014).ADSCrossRefGoogle Scholar
  10. 10.
    A. V. Shumilin and Y. M. Beltukov, arXiv:1904.03103.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Ioffe InstituteSt. PetersburgRussia

Personalised recommendations