Thermoelectric and viscous contributions to the hydrodynamic ratchet effect

We study the hydrodynamic regime of the ratchet effect, i.e., radiation-induced generation of a direct electric current ${J}_{\mathrm{rat}}$, in an asymmetric dual-grating gate structure without an inversion center. Recently, it was demonstrated that the frequency dependence of ${J}_{\mathrm{rat}}$ is essentially different within the hydrodynamic (HD) and drift-diffusion (DD) regimes of electron transport: ${J}_{\mathrm{rat}}^{\mathrm{HD}}\ensuremath{\propto}1/{\ensuremath{\omega}}^{6}$ and ${J}_{\mathrm{rat}}^{\mathrm{DD}}\ensuremath{\propto}1/{\ensuremath{\omega}}^{2}$ for $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$. Here, we analyze the previously neglected thermoelectric contribution to the ratchet current ${J}_{\mathrm{th}}$, which arises due to inhomogeneous heating of the electron liquid. We demonstrate that this contribution dominates at sufficiently low electron-phonon scattering rates, yields a high-frequency asymptotic ${J}_{\mathrm{th}}\ensuremath{\propto}1/{\ensuremath{\omega}}^{2}$ even in the HD regime, and can change the sign of the response at certain frequency intervals. We analyze the plasmonic resonance in ${J}_{\mathrm{rat}}$, which has the shape of an asymmetric Fano peak, and find that the asymmetry increases with increasing thermoelectric contribution. We also study the effect of finite viscosity of the electron liquid, as well as the manifestation of the plasmonic drag phenomena and inhomogeneous rectification effects in the ratchet current. We demonstrate that viscosity suppresses plasmonic resonance but unexpectedly enhances the Drude peak due to the interference nature of the ratchet effect.