Nonlinear hydrodynamic response of a quantum Hall system

The quantum Hall effect realizes a quantized Hall resistance R_xy = h/\(νe²\) 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_H. Here, we argue that a nonlinear relation between I and V_H could arise when the electric field is spatially inhomogeneous. We first discuss that the linear I-V_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.