Non-linear edge dynamics of an Integer Quantum Hall fluid

TL;DR

This paper presents a theoretical analysis of the nonlinear edge dynamics in an integer quantum Hall fluid, revealing new phenomena beyond traditional models, with implications for ultracold atomic gas experiments.

Contribution

It introduces a chiral nonlinear hydrodynamic model accounting for dispersion and curvature effects, extending the understanding of quantum Hall edge excitations.

Findings

Identification of a density-dependent velocity in edge dynamics

Observation of shock wave regularization into ripple patterns

Relevance for ultracold atomic gas experiments

Abstract

We report a theoretical study of the linear and nonlinear dynamics of edge excitations of an integer quantum Hall state of non-interacting fermions. New features beyond the chiral Luttinger liquid picture are anticipated to arise from the interplay of the curvature of the Landau level dispersion and of the Pauli exclusion principle. For long-wavelength perturbations, the microscopic numerical results are captured by a chiral nonlinear hydrodynamic equation including a density-dependent velocity term. In the wave-breaking regime, shock waves are found to be regularized into a complex ripple pattern by dispersion effects. Our results are of specific relevance for experiments with synthetic quantum matter, in particular ultracold atomic gases.