Nonreciprocity of hydrodynamic electron transport in noncentrosymmetric conductors

Abstract

We show that the nonreciprocity of hydrodynamic electron transport in noncentrosymmetric conductors with broken time-reversal symmetry (TRS) is significantly enhanced compared to the disorder-dominated regime. This enhancement is caused by the linear dependence of the viscosity of the electron liquid on the flow velocity, which is allowed in the absence of TRS and Galilean invariance. The resulting nonlinear flows break dynamical similarity and must be characterized by two dimensionless parameters: the Reynolds number and the emergent nonreciprocity number. The latter is linear in velocity but independent of system size. We determine the nonlinear conductance of a Hall bar and show that the nonreciprocal correction to the current can be of comparable magnitude to its reciprocal counterpart.

Figures (2)

• Figure 1: 2D nonreciprocal flow in a Hall bar of width $2d$. Nonreciprocal velocity profile $\bm{v}=u(y)\hat{\mathbf{x}}$ is controlled by the nonreciprocity number $\mathcal{N}$ in (\ref{['eq:nonreciprocity_number']}), which depends on the orientation of the in-plane magnetic field $B$ in vector-type symmetry breaking, and on the valley polarization and the orientation of the graphene lattice in tensor-type. Panel (a) displays the velocity profile (\ref{['eq:u-flow']}) for $\mathcal{N}=0.3$ and $0.9$, while panel (b) displays the velocity profiles for the time-reversed values $\mathcal{N}=-0.3$ and $-0.9$. In both cases the Poiseuille profile is restored for $\mathcal{N} \rightarrow 0$.
• Figure 2: Plot of the dimensionless current $I/I_0 = f(\mathcal{N})$ in Eq. (\ref{['eq:I']}) where $f$ is given by Eq. (\ref{['f']}), vs. the nonreciprocity number for positive branch ($\mathcal{N}>0$) and negative branch ($\mathcal{N}<0$) of the flow profile, cf. Fig. \ref{['fig:Hall-bar']}. The dashed line denotes its linear approximation, $I/I_0 \approx 1-\mathcal{N}/5$, whose nonreciprocal correction to the conductance was calculated in Eq. (\ref{['G2']}). At fixed bias, this shows the dependence of the nonlinear conductance on the TRS breaking strength.