Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets

TL;DR

This paper numerically investigates the edge dynamics of fractional quantum Hall droplets, revealing nonlinear effects and corrections to existing theories, with implications for experimental observation.

Contribution

It introduces a nonlinear chiral Luttinger liquid model capturing edge dynamics and nonlinear corrections in fractional quantum Hall systems.

Findings

Identification of cubic corrections to wave dispersion

Observation of broadening in dynamical structure factor

Sizable nonlinear effects in strong excitation regimes

Abstract

We report numerical studies of the linear and nonlinear edge dynamics of a non-harmonically confined macroscopic fractional quantum Hall fluid. In the long-wavelength and weak excitation limit, observable consequences of the fractional transverse conductivity are recovered. The first non-universal corrections to the chiral Luttinger liquid theory are then characterized: for a weak excitation in the linear response regime, cubic corrections to the linear wave dispersion and a broadening of the dynamical structure factor of the edge excitations are identified; for stronger excitations, sizable nonlinear effects are found in the dynamics. The numerically observed features are quantitatively captured by a nonlinear chiral Luttinger liquid quantum Hamiltonian that reduces to a driven Korteweg-de Vries equation in the semiclassical limit. Experimental observability of our predictions is finally discussed.