Hall field and odd viscosity in near-hydrodynamic electron flows

Abstract

In the presence of an applied magnetic field, the viscosity tensor of electron flows exhibits an off-diagonal component. This Hall or odd viscosity has recently been measured in high-mobility devices. It is known that use of the hydrodynamic theory to extract the Hall viscosity from Hall resistivity measurements strongly overestimates its value. We develop a general transport theory, using a matched asymptotic expansion of the kinetic equation in the near-hydrodynamic regime, and thereby investigate the origin of this discrepancy. This reveals that bulk, near-boundary and boundary condition corrections compete with the classical Hall (odd) viscosity. This finding reconciles the above-mentioned disparity and the transport theory we report provides a basis for future measurements.

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