Interaction induced edge channel equilibration

TL;DR

This paper investigates how Coulomb interactions induce energy exchange and equilibration between two chiral edge states in a quantum Hall system, highlighting the role of shot noise and providing analytic and numerical tools.

Contribution

It introduces an equation of motion approach to analyze edge state distribution functions and derives analytic expressions near a QPC, advancing understanding of edge channel equilibration.

Findings

Relaxation is driven by shot noise at the QPC.

Analytic expressions for distribution functions near the QPC.

Numerical method to compute distribution functions far from the QPC.

Abstract

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..