Scattering Mechanism in the Integer Quantum Hall Effect
We consider a large class of two-dimensional systems of electrons in a static disorder potential and subject to an in-plane electric field and to a strong perpendicular magnetic field. The time evolution of the single-particle states is investigated. It is found that the macroscopic Hall current is carried by the non-adiabatic states and that quantum Hall behavior occurs, when the Fermi energy lies in a range of adiabatic levels. Linear response theory is inadequate to describe the quantum mechanical scattering process of bulk states in the quantum Hall regime. The general results are illustrated by an explicit weak disorder model, where the scattering process and the nature of dc-insulating and -conducting states can be understood in detail. The time evolution of a scattered Landau function is calculated numerically. It gives a striking illustration of the velocity increase, due to disorder, of the conduction electrons in the bulk of a quantum Hall system. This phenomenon leads to current compensation, which is crucial for the IQHE. It is caused by a special kind of nonclassical particle propagation, which results from the nonlinear components of the single-particle currents. We believe that our results improve the present microscopic understanding of the IQHE.
Unable to display preview. Download preview PDF.
- 2.For a review see e. g. The Quantum Hall Effect, edited by R.E. Prange and S.M. Girvin (Springer-Verlag, New York, 1987).Google Scholar
- 3.M. Buttiker in Semiconductor and Semimetals in the volume Nanostructured Systems, ed. Mark A. Reed, (Academic Press, New York, 1990).Google Scholar
- 4.F. Kuchar, in Festkörperprobleme (Advances in Solid State Physics), edited by U. Rössler (Vieweg, Braunschweig 1988), Vol. 28, p. 45.Google Scholar
- 5.J. Riess, Phys. Rev. B38, 3133 (1988).Google Scholar
- 7.J. Riess, Phys. Rev. B41, 5251 (1990).Google Scholar
- 9.J. Riess and C. Duport, unpublished.Google Scholar
- 10.V. Gudmundsson and R. R. Gerhardts, in The Application of High Magnetic Fields in Semiconductor Physics II, Vol 87 of Springer Series in Solid State Sciences, edited by G. Landwehr (Springer, Berlin, 1989), and references therein.Google Scholar
- 11.R. B. Laughlin, Phys. Rev. B23. 5632 (1981); see also R. E. Prange, section 1.7 of Ref. 2.Google Scholar
- 12.For a review see D. J. Thouless, chapt. 4 of Ref. 2.Google Scholar