[Paper Review] Quantum feedback at the solid-liquid interface: flow-induced electronic current and its negative contribution to friction

Baptiste Coquinot, Lydéric Bocquet+1 more|arXiv (Cornell University)|May 6, 2022

Quantum and electron transport phenomena56 references4 citations

TL;DR

This paper develops a quantum-mechanical theory of hydrodynamic Coulomb drag at solid-liquid interfaces using the non-equilibrium Keldysh formalism, showing that flow-induced electronic currents arise from Coulomb interactions between liquid charge fluctuations (hydrons) and solid electrons, as well as electron-phonon coupling. The resulting current generates a quantum feedback effect that reduces hydrodynamic friction, providing a mechanism for controlling nanoscale fluid flow at the quantum level.

ABSTRACT

An electronic current driven through a conductor can induce a current in another conductor through the famous Coulomb drag effect. Similar phenomena have been reported at the interface between a moving fluid and a conductor, but their interpretation has remained elusive. Here, we develop a quantum-mechanical theory of the intertwined fluid and electronic flows, taking advantage of the non-equilibrium Keldysh framework. We predict that a globally neutral liquid can generate an electronic current in the solid wall along which it flows. This hydrodynamic Coulomb drag originates from both the Coulomb interactions between the liquid's charge fluctuations and the solid's charge carriers, and the liquid-electron interaction mediated by the solid's phonons. We derive explicitly the Coulomb drag current in terms of the solid's electronic and phononic properties, as well as the liquid's dielectric response, a result which quantitatively agrees with recent experiments at the liquid-graphene interface. Furthermore, we show that the current generation counteracts momentum transfer from the liquid to the solid, leading to a reduction of the hydrodynamic friction coefficient through a quantum feedback mechanism. Our results provide a roadmap for controlling nanoscale liquid flows at the quantum level, and suggest strategies for designing materials with low hydrodynamic friction.

Motivation & Objective

• To resolve the long-standing puzzle of flow-induced electronic currents in solid walls during liquid flow, particularly in ion-free systems where classical mechanisms fail.
• To develop a microscopic quantum theory of electronic current generation at solid-liquid interfaces, beyond macroscopic dielectric approximations.
• To identify the origin of the current as arising from two mechanisms: direct Coulomb coupling between liquid charge fluctuations (hydrons) and solid electrons, and electron-phonon coupling mediated by hydrodynamic friction.
• To demonstrate that this current generates a negative feedback on momentum transfer, thereby reducing the hydrodynamic friction coefficient.
• To provide a quantitative framework linking electronic and phononic properties of the solid and dielectric response of the liquid to the observed current and friction reduction.

Proposed method

• Employing the non-equilibrium Keldysh formalism to describe coupled electron and hydrodynamic degrees of freedom at the solid-liquid interface.
• Deriving the Keldysh susceptibility for electronic response using a quasi-equilibrium fluctuation-dissipation theorem, linking it to the retarded response function.
• Modeling the hydrodynamic Coulomb drag current as a result of two distinct mechanisms: direct Coulomb interaction with hydrons and electron-phonon coupling via liquid-induced phonon excitation.
• Computing the electron-boson friction force using Keldysh correlation functions, with non-equilibrium effects incorporated through a differential velocity dependence.
• Establishing a scaling law for the friction coefficient in terms of electronic density, effective mass, and Fermi wavevector, validated against numerical results.
• Using the formalism to derive a closed-form expression for the friction coefficient that depends on the solid’s electronic and phononic response and the liquid’s dielectric function.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the flow-induced electronic current in a solid wall during liquid flow, particularly in the absence of net charge or ion transport?
• RQ2 How do Coulomb interactions between liquid charge fluctuations (hydrons) and solid electrons contribute to current generation at the interface?
• RQ3 To what extent do electron-phonon coupling mechanisms, driven by hydrodynamic friction, contribute to the observed current?
• RQ4 How does the generated electronic current feedback to reduce the hydrodynamic friction coefficient?
• RQ5 What is the quantitative dependence of the friction coefficient on the electronic and phononic properties of the solid and the dielectric response of the liquid?

Key findings

• A globally neutral liquid can generate a net electronic current in a solid wall via hydrodynamic Coulomb drag, driven by Coulomb interactions with liquid charge fluctuations (hydrons).
• The theory predicts a negative contribution to hydrodynamic friction due to the feedback of the induced electronic current, reducing the effective friction coefficient.
• The current arises from two distinct mechanisms: direct Coulomb coupling between hydrons and electrons, and electron-phonon coupling mediated by liquid flow.
• The friction coefficient scales as $\lambda_{\rm b/e} \propto m^{2}\mu$ for a 2D electron gas, and $\lambda_{\rm b/e} \propto n^{3/2}$ in graphene for hydron interactions, consistent with numerical simulations.
• The theory quantitatively agrees with recent experiments at the liquid-graphene interface, validating the proposed quantum feedback mechanism.
• The electron-boson friction coefficient remains expressible in quasi-equilibrium form even under non-equilibrium conditions, provided the fluctuation-dissipation relation holds.