Density of states, screening and the width of the quantum Hall plateaus

TL;DR

This paper develops a consistent electrostatic model of the quantum Hall effect, deriving a modified density of states that explains the temperature dependence and width of quantum Hall plateaus, and impacts electron relaxation processes.

Contribution

It introduces a new form of the density of states for interacting electrons in the quantum Hall regime, explaining experimental observations of plateau widths and temperature effects.

Findings

Derived a non-gaussian density of states for quantum Hall electrons.

Identified a crossover temperature affecting the validity of the model.

Showed the density of states enhances electron-lattice relaxation rates.

Abstract

We present a consistent treatment of the quantum Hall effect within the electrostatic approximation. We derive the form of the density of states (DOS) which differs from the usual gaussian shape valid for non-interacting electrons. Below a crossover temperature, this DOS gradually transforms into the non-interacting DOS near the Fermi energy. We obtain an estimate of this crossover temperature, which determines the range of validity of this framework, and allows a reconciliation of the width and temperature dependence of the quantum Hall plateaus with experiments. The DOS dramatically enhances the electron-lattice relaxation rate, thus reducing the possibility of electron overheating.