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A. Endo, N. Hatano, H. Nakamura and R. Shirasaki
Fundamental Relaton between Longitudinal and Transverse Conductivities in the Quantum Hall System
Date of publication:
July 09, 2009
conductivity tensor, two-dimensional electron system, GaAs; Al-GaAs, long range impurity potential
We investigate the relation between the diagonal (σxx) and off-diagonal (σxy) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy 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 Bσ2xx. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.
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