Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime

TL;DR

This paper develops a detailed formalism for analyzing equilibrium properties and dissipation in disordered two-dimensional electron gases under high magnetic fields, incorporating Landau level mixing and wave function broadening effects.

Contribution

It introduces a recursive high magnetic field expansion for Green's functions that accounts for smooth potentials, enabling detailed microscopic analysis of transport and dissipation.

Findings

Derived Green's functions up to order l_B^3 for arbitrary smooth potentials.

Provided microscopic expressions for local charge, current densities, and conductivity tensor.

Validated the theory against exact solutions, demonstrating controlled accuracy.

Abstract

We develop in detail a new formalism [as a sequel to the work of T. Champel and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for treating quantum problems involving slowly-varying potentials at high magnetic fields in two-dimensional electron gases. For an arbitrary smooth potential we show that electronic Green's function is fully determined by closed recursive expressions that take the form of a high magnetic field expansion in powers of the magnetic length l_B. For illustration we determine entirely Green's function at order l_B^3, which is then used to obtain quantum expressions for the local charge and current electronic densities at equilibrium. Such results are valid at high but finite magnetic fields and for arbitrary temperatures, as they take into account Landau level mixing processes and wave function broadening. We also check the accuracy of our general functionals against the exact solution of a one-dimensional parabolic confining potential, demonstrating the controlled character of the theory to get equilibrium properties. Finally, we show that transport in high magnetic fields can be described hydrodynamically by a local equilibrium regime and that dissipation mechanisms and quantum tunneling processes are intrinsically included at the microscopic level in our high magnetic field theory. We calculate microscopic expressions for the local conductivity tensor, which possesses both transverse and longitudinal components, providing a microscopic basis for the understanding of dissipative features in quantum Hall systems.