Real-time diagrammatic approach to current-induced forces: Application to quantum-dot based nanomotors

In recent years there has been increasing excitement regarding nanomotors and particularly current-driven nanomotors. Despite the broad variety of stimulating results found, the regime of strong Coulomb interactions has not been fully explored for this application. Here we consider nanoelectromechanical devices composed of a set of coupled quantum dots interacting with mechanical degrees of freedom taken in the adiabatic limit and weakly coupled to electronic reservoirs. We use a real-time diagrammatic approach to derive general expressions for the current-induced forces, friction coefficients, and zero-frequency force noise in the Coulomb blockade regime of transport. We prove our expressions obey Onsager's reciprocity relations and the fluctuation-dissipation theorem for the energy dissipation of the mechanical modes. The obtained results are illustrated with a nanomotor consisting of a double quantum dot capacitively coupled to rotating charges. We analyze the dynamics and performance of the motor as a function of the applied voltage and loading force for trajectories encircling different triple points in the charge stability diagram.