Local density of states of two-dimensional electron systems under strong in-plane electric and perpendicular magnetic fields

TL;DR

This paper investigates how strong in-plane electric and perpendicular magnetic fields affect the local density of states in two-dimensional electron systems, revealing broadening of Landau levels and implications for the quantum Hall effect.

Contribution

It provides analytical models for the local density of states under crossed fields and discusses their relevance to quantum Hall breakdown phenomena.

Findings

Electric fields broaden Landau level peaks

Overlap of peaks indicates inter-Landau-level scattering

Modeling of incompressible stripes and screening effects

Abstract

We calculate the local density of states of a two-dimensional electron system under strong crossed magnetic and electric fields. We assume a strong perpendicular magnetic field which, in the absence of in-plane electric fields and collision broadening effects, leads to Landau quantization and the well-known singular Landau density of states. Unidirectional in-plane electric fields lead to a broadening of the delta-function-singularities of the Landau density of states. This results in position-dependent peaks of finite height and width, which can be expressed in terms of the energy eigenfunctions. These peaks become wider with increasing strength of the electric field and may eventually overlap, which indicates the onset of inter-Landau-level scattering, if electron-impurity scattering is considered. We present analytical results for two simple models and discuss their possible relevance for the breakdown of the integer quantized Hall effect. In addition, we consider a more realistic model for an incompressible stripe separating two compressible regions, in which nearly perfect screening pins adjacent Landau levels to the electrochemical potential. We also discuss the effect of an imposed current on the local density of states in the stripe region.