
Author(s):
A. Endo, N. Hatano, H. Nakamura and R. Shirasaki

Title:
Fundamental Relaton between Longitudinal and Transverse Conductivities in the Quantum Hall System

Date of publication:
July 09, 2009

Key words:
conductivity tensor, twodimensional electron system, GaAs; AlGaAs, long range impurity potential

Abstract:
We investigate the relation between the diagonal (σxx) and offdiagonal (σxy) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a shortrange impurity potential using the linear response theory, employing an approximation that simply replaces the selfenergy by a constant value ih/(2τ) with the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width Γ = h/(2τ). Analytic formulas are obtained for bothσxx and σxy within the framework of this simple approximation at low temperatures. By examining the leading terms in σxx andσxy, we find a proportional relation between dσxy /dB and Bσ^{2}xx. The relation, after slight modification to account for the longrange nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs twodimensional electron system at the low magneticfield regime where spin splitting is negligibly small.
