Effect of quantum hopping on the Coulomb gap of localized electrons in disordered systems

G. Vignale; Y. Shinozuka; W. Hanke

doi:10.1103/PhysRevB.34.3003

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Effect of quantum hopping on the Coulomb gap of localized electrons in disordered systems

G. Vignale and Y. Shinozuka^*

W. Hanke

Max-Planck-Institut für Festkörperforschung, D-7000 Stuttgart 80, Federal Republic of Germany

Physikalisches Institut, Universität Würzburg, D-8700 Würzburg, Federal Republic of Germany

^*Permanent address: Faculty of Engineering, Yamaguchi University, Tokiwadai Ube 755, Japan.

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Phys. Rev. B 34, 3003(R) – Published 15 August, 1986

DOI: https://doi.org/10.1103/PhysRevB.34.3003

Abstract

We study the effect of quantum hopping on the one-particle density of states of a system of localized electrons interacting with each other via the long-range Coulomb force. It is found that (1) contrary to the previous classical theories, there is no Coulomb gap in two dimensions, in agreement with recent experiments on doped Si inversion layers, and (2) in three dimensions the Coulomb gap is first reduced in width and then disappears when the hopping rate exceeds a critical value. This reduction of the Coulomb gap is discussed in connection with the reduction of the effective interaction between localized quasiparticles.

References (13)

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[c1] A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 (1975)

[c2] A. L. Efros, J. Phys. C 9, 2021 (1976) B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Berlin, 1984)

[c3] Electron-Electron Interaction in Disordered Systems, edited by A. L. Efros and M. Pollak (North-Holland, Amsterdam, 1985)

[c4] S. D. Baranovskii, A. L. Efros, B. L. Gelmont, and B. I. Shklovskii, J. Phys. C 12, 1023 (1979)

[c5] M. Grünewald, B. Pohlman, L. Schweitzer, and D. Würtz, J. Phys. C 15, L1153 (1982)

[c6] J. H. Davies, P. A. Lee, and T. M. Rice, Phys. Rev. B 29, 4260 (1984)

[c7] M. Pollak, Discuss. Faraday Soc. 50, 13 (1970)

[c8] G. Srinivasan, Phys. Rev. B 4, 2581 (1971)

[c9] G. Timp, A. B. Fowler, A. Hartstein, and P. N. Butcher, Phys. Rev. B 33, 1499 (1986)

[c10] W. N. Shafarman and T. G. Castner, Phys. Rev. B 33, 3570 (1986)

[c11] G. Timp and A. B. Fowler, Phys. Rev. B 33, 4392 (1986)

[c12] V. Velicky, S. Kirkpatrick, and H. Ehrenreich, Phys. Rev. 175, 747 (1968)

[c13] F. Yonezawa and K. Morigaki, Suppl. Prog. Theor. Phys. 53, 1 (1973)

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Effect of quantum hopping on the Coulomb gap of localized electrons in disordered systems

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