Quantum transport properties of two-dimensional electron gases under high magnetic fields

TL;DR

This paper develops a vortex state formalism within real-time Green functions to analyze quantum transport in 2D electron gases under high magnetic fields, deriving Hall conductance quantization and discussing dissipative effects.

Contribution

It introduces a vortex state approach in the Keldysh formalism for finite magnetic fields, extending high-field expansion methods beyond the semi-classical limit.

Findings

Derived vortex current density in the presence of magnetic fields.

Expressed total current as edge contributions only.

Quantified Landau-level mixing effects on Hall conductance.

Abstract

We study quantum transport properties of two-dimensional electron gases under high perpendicular magnetic fields. For this purpose, we reformulate the high-field expansion, usually done in the operatorial language of the guiding-center coordinates, in terms of vortex states within the framework of real-time Green functions. These vortex states arise naturally from the consideration that the Landau levels quantization can follow directly from the existence of a topological winding number. The microscopic computation of the current can then be performed within the Keldysh formalism in a systematic way at finite magnetic fields $B$ (i.e. beyond the semi-classical limit $B = \infty$). The formalism allows us to define a general vortex current density as long as the gradient expansion theory is applicable. As a result, the total current is expressed in terms of edge contributions only. We obtain the first and third lowest order contributions to the current due to Landau-levels mixing processes, and derive in a transparent way the quantization of the Hall conductance. Finally, we point out qualitatively the importance of inhomogeneities of the vortex density to capture the dissipative longitudinal transport.