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Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice. II. Arbitrary electric field directions

Andrey R. Kolovsky1,2, Ilya Chesnokov2, and Giorgio Mantica3,4,5

  • 1Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia
  • 2Siberian Federal University, 660041 Krasnoyarsk, Russia
  • 3Center for Nonlinear and Complex Systems, Department of Science and High Technology, University of Insubria, 22100 Como, Italy
  • 4I.N.F.N. sezione di Milano, Italy
  • 5CNISM unità di Como, Italy

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Phys. Rev. E 86, 041146 – Published 25 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041146

Abstract

We study the quantum dynamics of a charged particle in a two-dimensional lattice, subject to constant and homogeneous electric and magnetic fields. We find that different regimes characterize these motions, depending on a combination of conditions, corresponding to weak and strong electric field intensities, rational or irrational directions of the electric field with respect to the lattice, and small or large values of the magnetic (Peierls) phase.

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See Also

Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice

Andrey R. Kolovsky and Giorgio Mantica
Phys. Rev. E 83, 041123 (2011)

Article Text

References (17)

  1. A. R. Kolovsky and G. Mantica, Phys. Rev. E 83, 041123 (2011).
  2. T. Nakanishi, T. Ohtsuki, and M. Saitoh, J. Phys. Soc. Jpn. 64, 2092 (1995).
  3. A. Barelli, J. Bellissard, and F. Claro, Phys. Rev. Lett. 83, 5082 (1999).
  4. H. N. Nazareno and P. E. de Brito, Phys. Rev. B 64, 045112 (2001).
  5. E. Muñoz, Z. Barticevic, and M. Pacheco, Phys. Rev. B 71, 165301 (2005).
  6. H. N. Nazareno, P. E. de Brito, and E. S. Rodrigues, Phys. Rev. B 76, 125405 (2007).
  7. By varying this ratio, interesting dynamical effects can be found: R. Ketzmerick, K. Kruse, D. Springsguth, and T. Geisel, Phys. Rev. Lett. 84, 2929 (2000). Notice that this paper is limited to the case of null electric field.
  8. J. Bellissard, R. Lima, and E. Scoppola, Commun. Math. Phys. 88, 465 (1983).
  9. J. Bellissard, in Trends and Developments in the Eighties, edited by S. Albeverio and Ph. Blanchard (World Scientific Pub. Co., Singapore, 1985).
  10. J. Bellissard, in Stochastic Processes in Classical and Quantum Systems (Ascona, 1985), Lecture Notes in Physics, Vol. 262 (Springer, Berlin, 1986), p. 2438.
  11. In Ref. [1] we restricted ourselves by considering g(κ)=1 if π(2n−1)/a≤κ<π(2n+1)/a and zero otherwise.
  12. A graphic representation of these bands is widely known as Hofstadter's butterfly; see D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
  13. G. Mantica, in Applications and Computation of Orthogonal Polynomials, edited by W. Gautschi , Internat. Ser. Numer. Math., Vol. 131 (Birkhäuser, Basel, 1999), p. 153.
  14. J. Bellissard (private communication).
  15. We need to remark in this respect that our analysis did not confirm in the long-time run the results of Nazareno et al. [4], who claimed localization for the case (r,q)=(1,1) and α=1/2.
  16. I. Guarneri and G. Mantica, Phys. Rev. Lett. 73, 3379 (1994).
  17. G. Mantica, Electron. Trans. Numer. Anal. 25, 409 (2006).

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Phys. Rev. E 86, 041146– Published 25 October, 2012
  • Received 25 May 2012

©2012 American Physical Society

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