Efficiency of determinantal transport theory in the integer quantum Hall effect

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Abstract
A steady-state solution of the density matrix, capable of properly handling a quasi-infinite density of states, is applied to the integer quantum Hall effect in a noninteracting two-dimensional electron gas, on the basis of unperturbed Landau’s states. The width of the Landau subbands due to the crystal periodic potential is taken as an infinitely small quantity tending to zero, and the initial many-body density matrix at equilibrium is calculated up to first order of this bandwidth. This allows us to extract the finite principal part of the conductivity-tensor components from the statistical average of the current density. The quantized plateaus of the Hall conductivity are shown to result from both the very large relaxation parameters due to the quasi-infinite density of states in the Landau subbands and the effect of disorder on the center-of-orbit motion. These are responsible for the vanishing of the diagonal conductivity, except in the intermediate regions between the plateaus, where the density of states is strongly reduced and additional interband transitions take place. The present treatment formally amounts to a change of basis and explains that the underlying physical content is found to be in agreement with prevailing interpretations. The salient experimental features are obtained without an explicit knowledge of localized-extended states, nor with the use of gauge or topological invariants. Owing to its efficiency and simplicity, such an approach offers attractive promise in further quantitative developments.