Solitons on the edge of a two-dimensional electron system

TL;DR

This paper investigates non-linear excitations called solitons on the edge of a 2D electron system in a magnetic field, revealing rotating shape solutions relevant to quantum Hall edge modes.

Contribution

It introduces a non-linear contour dynamics approach that uncovers soliton solutions on the edge of a 2D electron droplet, extending beyond linear approximations.

Findings

Discovery of soliton solutions as rotating shapes

Derivation of a modified Korteweg-de Vries equation for edge dynamics

Application to quantum Hall edge mode phenomena

Abstract

We present a study of the excitations of the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the non-linear analysis yields soliton solutions which correspond to uniformly rotating shapes. These modes are found from a perturbative treatment of a non-linear eigenvalue problem, and as solutions to a modified Korteweg-de Vries equation resulting from a local induction approximation to the nonlocal contour dynamics. We discuss applications to the edge modes in the quantum Hall effect.