# Exact Widths and Tails for Landau Levels Broadened by a Random Potential with an Arbitrary Correlation Length

• K. Broderix
• N. Heldt
• H. Leschke
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 101)

## Abstract

This publication is concerned with the broadening of Landau levels due to disorder and some effects thereof. The underlying model can be described by the Hamiltonian
$$\begin{array}{*{20}c} {H: = H_0 + V,} & {H_0 : = \frac{1} {{2m}}\left( {\frac{{\hbar \partial }} {{i\partial x_1 }}} \right)^2 + \frac{1} {{2m}}\left( {\frac{{\hbar \partial }} {{i\partial x_2 }} + eBx_1 } \right)^2 } \\ \end{array}$$
(1)
(1) for one (spinless) electron of (effective) mass m and charge −e in the infinite (x 1,x 2) plane under the influence of a perpendicular constant magnetic field of strength B and a random potential V. The probability distribution of V is assumed to be Gaussian with
$$\begin{array}{*{20}c} {\overline {V\left( x \right)} = 0,} & {\overline {V\left( x \right)V\left( {x'} \right)} = \sigma ^2 \exp \left\{ {{{ - \left( {x - x'} \right)^2 } \mathord{\left/ {\vphantom {{ - \left( {x - x'} \right)^2 } {2\lambda }}} \right. \kern-\nulldelimiterspace} {2\lambda }}^2 } \right\},} & {x: = \left( {x_1 ,x_2 } \right).} \\ \end{array}$$
(2)
(2) Here the overbar denotes the average with respect to the probability distribution, σ is the strength and λ the correlation length of the fluctuations of the potential.

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