Simple models suffice for the single dot quantum shuttle

TL;DR

This paper demonstrates that simple models can effectively describe different charge transport regimes in a quantum shuttle device, providing clear physical insights and matching complex numerical solutions within their valid domains.

Contribution

It introduces simplified equations for the three charge transport regimes in a quantum shuttle, making analysis more accessible and interpretable compared to full numerical solutions.

Findings

Simplified models accurately describe each transport regime.

Clear physical interpretation of charge transport mechanisms.

Good agreement with full numerical solutions within validity domains.

Abstract

A quantum shuttle is an archetypical nanoelectromechanical device, where the mechanical degree of freedom is quantized. Using a full-scale numerical solution of the generalized master equation describing the shuttle, we have recently shown [Novotn\'{y} {\it et al.}, Phys. Rev. Lett. {\bf 92}, 248302 (2004)] that for certain limits of the shuttle parameters one can distinguish three distinct charge transport mechanisms: (i) an incoherent tunneling regime, (ii) a shuttling regime, where the charge transport is synchronous with the mechanical motion, and (iii) a coexistence regime, where the device switches between the tunneling and shuttling regimes. While a study of the cross-over between these three regimes requires the full numerics, we show here that by identifying the appropriate time-scales it is possible to derive vastly simpler equations for each of the three regimes. The simplified equations allow a clear physical interpretation, are easily solved, and are in good agreement with the full numerics in their respective domains of validity.