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

TL;DR

This paper develops a real-time diagrammatic method to analyze current-induced forces in quantum-dot nanomotors, especially under strong Coulomb interactions, and demonstrates its application to a double quantum dot nanomotor's dynamics.

Contribution

It introduces a novel approach for calculating forces and noise in Coulomb blockade regimes and applies it to analyze nanomotor performance.

Findings

Derived general expressions satisfying Onsager's relations.

Validated the approach in a double quantum dot nanomotor model.

Analyzed motor dynamics under various voltages and forces.

Abstract

During the last years there has been an increasing excitement in nanomotors and particularly in 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 by 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 accomplish with Onsager's reciprocity relations and the fluctuation-dissipation theorem for the energy dissipation of the mechanical modes. The obtained results are illustrated in a nanomotor consisting of a double quantum dot capacitively coupled to some rotating charges. We analyze the dynamics and performance of the motor as function of the applied voltage and loading force for trajectories encircling different triple points in the charge stability diagram.