Odd viscosity and anomalous Hall effect in two dimensional electron systems with smooth disorder

Abstract

A microscopic theory of odd viscosity in two-dimensional electron systems with smooth disorder and spin-orbit interaction is developed. It is shown that spin-orbit scattering gives rise to an off-diagonal component of the viscosity tensor. Hydrodynamic equations for spin and electric currents are derived for electrons interacting with smooth disorder. The contribution of odd viscosity to the anomalous Hall effect is calculated.

Figures (2)

• Figure 1: The graph shows the dependence of odd viscosity $\eta_{xy,SO}$ (blue line) in the case of a Gaussian impurity potential \ref{['Odd viscosity: U_c,v gauss']} on the screening parameter $k_Fr_0$. The odd viscosity is normalized to its asymptotic value $\eta_{xy,SO}^{gauss}$\ref{['Odd viscosity: eta_xy,SO^gauss']} at $k_Fr_0 \rightarrow \infty$. The "effective" odd viscosity $\eta_{xy,SO}^H$ (red line), which enters the expression for the Hall field \ref{['Hall effect: E_H^a']}, is also shown.
• Figure 2: Schematic of an electron channel, infinite along the $y$ axis and of width $w$ along the $x$ axis. The electric field is directed along the channel ($\bm E \parallel y$), the magnetic field is perpendicular to the plane of particle motion ($\bm B \parallel z$). The Hall effect leads to charge accumulation at the channel edges and $\bm E_H \parallel x$. The figure shows the parabolic current profile along the channel in the limit of hydrodynamic electron transport.