Related papers: Nonlinear hydrodynamic response of a quantum Hall system

Nonlinear hydrodynamic response of a quantum Hall system

URL: http://arxiv.org/abs/2603.29390v1
Date: Tue, 31 Mar 2026 07:56:17 GMT
Title: Nonlinear hydrodynamic response of a quantum Hall system
Abstract summary: The quantum Hall effect realizes a quantized Hall resistance $R_xy = h/(e2)$ whereas the longitudinal resistance vanishes.<n>High precision measurements of $R_xy$ allude to a linear relation between the applied current $I$ and the Hall voltage $V_mathrmH$.
Score: 0.0
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(νe^2)$ 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 $ν$. 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.

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