Nonlinear hydrodynamic response of a quantum Hall system

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.

8+10 pages, 2+1 figures

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