Self-consistent local-equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

TL;DR

This paper develops a self-consistent local-equilibrium model to explain the spatial distribution of dissipative currents and electrostatic potential in a Hall bar under strong magnetic fields, aligning theory with recent experimental observations.

Contribution

It introduces a generalized Thomas-Fermi--Poisson approach for local equilibrium, incorporating finite electrochemical potential gradients to model dissipative currents in quantum Hall systems.

Findings

Current density localizes near incompressible strips.

Location and width of current-carrying strips depend on applied current.

Model aligns with experimental spatial current distributions.

Abstract

Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the edges of the Hall bar, cannot be understood on the basis of existing equilibrium theories. To explain these experiments, we generalize the Thomas-Fermi--Poisson approach for the self-consistent calculation of electrostatic potential and electron density in {\em total} thermal equilibrium to a {\em local equilibrium} theory that allows to treat finite gradients of the electrochemical potential as driving forces of currents in the presence of dissipation. A conventional conductivity model with small values of the longitudinal conductivity for integer values of the (local) Landau-level filling factor shows that, in apparent agreement with experiment, the current density is localized near incompressible strips, whose location and width in turn depend on the applied current.