Quantum Feedback at the Solid-Liquid Interface: Flow-Induced Electronic Current and Its Negative Contribution to Friction

An electronic current driven through a conductor can induce a current inanother conductor through the famous Coulomb drag effect. Similar phenomenahave been reported at the interface between a moving fluid and a conductor, buttheir interpretation has remained elusive. Here, we develop aquantum-mechanical theory of the intertwined fluid and electronic flows, takingadvantage of the non-equilibrium Keldysh framework. We predict that a globallyneutral liquid can generate an electronic current in the solid wall along whichit flows. This hydrodynamic Coulomb drag originates from both the Coulombinteractions between the liquid's charge fluctuations and the solid's chargecarriers, and the liquid-electron interaction mediated by the solid's phonons.We derive explicitly the Coulomb drag current in terms of the solid'selectronic and phononic properties, as well as the liquid's dielectricresponse, a result which quantitatively agrees with recent experiments at theliquid-graphene interface. Furthermore, we show that the current generationcounteracts momentum transfer from the liquid to the solid, leading to areduction of the hydrodynamic friction coefficient through a quantum feedbackmechanism. Our results provide a roadmap for controlling nanoscale liquid flowsat the quantum level, and suggest strategies for designing materials with lowhydrodynamic friction.