Nonlinear hydrodynamic response of a quantum Hall system

TL;DR

This paper investigates the nonlinear hydrodynamic response in quantum Hall systems, showing that inhomogeneous electric fields can induce nonlinear relations between current and Hall voltage due to fluid dynamics effects.

Contribution

It introduces a hydrodynamic framework to explain nonlinear electrical responses in quantum Hall liquids caused by spatial electric field inhomogeneities.

Findings

Linear I-V_H relation holds under Galilean invariance.

Nonlinear response arises from centrifugal forces and density gradients in curved flow.

Hydrodynamic effects can lead to nonlinear Hall responses in inhomogeneous fields.

Abstract

The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(\nu e^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck constant $h$, along with an integer or fractional constant $\nu$. High precision measurements of $R_{xy}$ allude to a linear relation between the applied current $I$ and the Hall voltage $V_\mathrm{H}$. Here, we argue that a nonlinear relation between $I$ and $V_\mathrm{H}$ could arise when the electric field is spatially inhomogeneous. We first discuss that the linear $I$-$V_\mathrm{H}$ relation holds with Galilean invariance. Then we consider a hydrodynamic description of a quantum Hall liquid to deal with an axially symmetric electric field. It reveals a nonlinear electronic response arising from the centrifugal force exerted on a curved flow and the density gradient invoked by vorticity.