Relaxation in driven integer quantum Hall edge states

TL;DR

This paper presents an exact theoretical model for relaxation phenomena in driven quantum Hall edge states at filling factor 2, accurately explaining experimental observations of non-thermal electron distributions relaxing downstream.

Contribution

It provides the first exact solution for the relaxation dynamics in a minimal model of quantum Hall edge states at filling factor 2, aligning well with experimental data.

Findings

The model reproduces the observed relaxation length and distribution shapes.

It demonstrates the non-thermal to stationary distribution transition.

The results validate the minimal model's applicability to real systems.

Abstract

A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor \nu=2, with results that account well for the observations.