Voltage-tunable nonequilibrium dispersion interactions

We develop a nonequilibrium Green's function theory for dispersion interactions between two nanostructures, each an open quantum system driven into a nonequilibrium steady state by an applied bias voltage. Starting from the two-particle nonequilibrium Green's function, we derive a general expression for the interaction energy in terms of the polarization propagators of the individual systems. The interaction energy admits a physically transparent decomposition into charge noise and charge dissipation contributions, providing a fluctuation-dissipation interpretation that generalizes the equilibrium London picture. Model calculations for coupled molecular junctions demonstrate that the applied voltage can enhance the attractive dispersion interaction by nearly an order of magnitude relative to equilibrium. In thermal equilibrium, the dispersion interaction is universally attractive, irrespective of the specific form of the nanostructure Hamiltonians or their coupling to reservoirs. Out of equilibrium, we introduce a generalized Kubo-Martin-Schwinger ratio that parameterizes the departure from detailed balance. We show that, in contrast to equilibrium, nonequilibrium conditions can lead to a repulsive dispersion interaction. Finally, we discuss the conditions under which population inversion in the electronic leads can drive a sign reversal of the dispersion interaction.