Electron density of states and localization of two-dimensional disordered systems in quantized magnetic fields
Кілттік сөздер:
electron conductivity, critical phenomena, two-dimensional electron gas, quantum Hall effect, electron localizationАннотация
We study numerically non-interacting electrons moving on a two-dimensional lattice with a uniform magnetic field and a random site potential. The electron localization and the density of states are investigated by using the method of transfer-matrices and by the direct diagonalization technique. For numerical simulations the Ando model with the diagonal disorder is used. The first preliminary data have been obtained for different sizes of the system and various values of the magnetic field. The localization length exhibits Shubnikov-de-Haas oscillations. The density of states shows several Landau bands separated by the energy gaps. With increasing the disorder the Landau bands becomes broader and overlap with each other. The application of the obtained results to the integer quantum Hall effect is discussed.
Библиографиялық сілтемелер
2 Klitzing von K., Ebert G. – In: Two-dimensional systems, Heterostuctures and Superlatiices / Ed. By G. Bauer, F. Kuchar, H. Heinrich. Berlin - Heidelberg – N.Y. – Tokyo, 1984, p. 243-252.
3 Tsui D.C., Stormer H.L., Gossard A.C. Fractional quantum Hall effect // Phys. Rev. Lett. 1982. – V. 48, N. 22. – P. 1559-1562.
4 Prange R.and Girvin S. The Quantum Hall Effect // Springer Verlag, Berlin. 1990. – 213p.
5 Hajdu J. Introduction to the Theory of the Quantum Hall Effect. VCH Verlag. 1994. – 308p.; Klitzing von K, Ebert G. Physica 1983. - V. 117B/118B. - P. 682-687.
6 Wegner F.J. Disordered system with n orbitals per site: n = ∞ limit // Phys. Rev. B. 1979. – V. 19. – P. 783-788.
7 Wegner F.J. Electrons in disordered systems. Scaling near the mobility edge // Z. Phys. B. 1976. – V. 25. – P. 327-337.
8 Wigner E.P. On the statistical distribution of widths and spacings of nuclear resonance levels // Proc. Cambridge Phil. Soc. – 1951. – Vol.47. – P. 790-798.
9 Dyson F.J. Statistical theory of the energy levels of complex systems // J. Math. Phys. 1962. – V.3. – P. 140-157.
10 Mehta M.L. Random Matrices // 2nd ed. Academic Press, Boston, 1991, 523p.
11 Kramer B. and MacKinnon A. Localization: theory and experiment // Rep. Prog. Phys. 1994. – V. 56. – P. 1469 -1601.
12 Gor’kov L.P. and Eliashberg G.M. Small metallic particles in the electromagnetic field // Zh. Eksp. Teor. Fiz. 1965. – V. 48. – P. 1407-1418.
13 Gutzwiller M. C. Chaos in Classical and Quantum Mechanics, Interdisciplinary Applied Mathematics. – V.1. - Springer, New York, 1990, 433p.
14 Haake F. Quantum Signatures of Chaos, Springer Series in Synergetics, ed. H. Haken. – V.54. - Berlin, 1991, 349p.
15 Efetov K. B. Supersymmetry and theory of disordered metals // Adv. Phys. – 1983. – V. 32, N.1 – P. 53-127.
16 Ando T. Numerical study of symmetry effects on localization in two dimensions // Phys Rev. B. 1989. – V. 40. – P. 5325-5329.
17 Batsch M., Schweitzer L., Zharekeshev I. Kh., Kramer B. Crossover from critical orthogonal to critical unitary statistics at the Anderson transition // Phys. Rev. Lett. – 1996. – V.77. – P. 1552-1555.
18 Dröse T., Batsch M., Zharekeshev I.Kh., Kramer B. Phase diagram of localization in a magnetic field // Phys. Rev. B. – 1998. – V.57. – P. 37-40.
19 Zharekeshev, I.Kh. Localization trajectory and critical index // Vestnik KazNU. Seriya Fizicheskaya. – 2010. – V.32, N.1. – P. 51–55.
20 Zharekeshev, I.Kh. Level statistics and phase diagram for the quantum Hall effect // Abstr. Meeting of the APS. – Montreal, Canada, 2004. – P. R1265.
