Thermoelectric and viscous contributions to the hydrodynamic ratchet effect

We study thermoelectric and viscous contributions to the ratchet effect, i.e. radiation-induced generation of the direct electric current, Jᵣₐₜ, in asymmetric dual-grating gate structure without inversion center. Previously [E.M\"onch et al, Phys. Rev. B { 105}, 045404 (2022)], it was demonstrated that frequency dependence of the Jᵣₐₜ is essentially different within hydrodynamic (HD) and drift-diffusion (DD) regimes of the electron transport: JᵣₐₜHD ∝ 1/ω⁶ and JᵣₐₜDD ∝ 1/ω² for ω → ∞. Here we analyze previously neglected thermoelectric contribution and find that it yields high-frequency asymptotic 1/ω² even in the HD regime and can change sign of the response. Account of the finite viscosity of the electron liquid yields contribution which scales at high frequency as 1/ω⁴. We also find plasmonic resonances in the Jᵣₐₜ, and demonstrate that asymmetry of the structure allows for excitation of the so-called directional travelling plasmons.