Local density of states in disordered two-dimensional electron gases at high magnetic field

TL;DR

This paper provides an exact solution for the local density of states in disordered two-dimensional electron gases under high magnetic fields, revealing universal geometric dependencies and the significance of thermal effects near saddle points.

Contribution

It introduces a novel analytical method using coherent state Green's functions to exactly determine the LDoS in arbitrary smooth potentials at high magnetic fields.

Findings

LDoS depends universally on local geometric properties like drift velocity and potential curvature.

Thermal effects cause significant broadening of tunneling trajectories near saddle points.

The approach treats confining and open quantum systems on equal footing.

Abstract

Motivated by high-accuracy scanning tunneling spectroscopy measurements on disordered two-dimensional electron gases in strong magnetic field, we present an exact solution for the local density of states (LDoS) of electrons moving in an arbitrary potential smooth on the scale of the magnetic length, that can be locally described up to its second derivatives. We use a technique based on coherent state Green's functions, allowing us to treat on an equal footing confining and open quantum systems. The energy-dependence of the LDoS is found to be universal in terms of local geometric properties, such as drift velocity and potential curvature. We also show that thermal effects are quite important close to saddle points, leading to an overbroadening of the tunneling trajectories.