Multiscale Modeling of a Nanoelectromechanical Shuttle

In this article, we report a theoretical analysis of a nanoelectromechanical shuttle based on a multiscale model that combines microscopic electronic structure data with macroscopic dynamics. The microscopic part utilizes a (static) density functional description to obtain the energy levels and orbitals of the shuttling particle together with the forces acting on the particle. The macroscopic part combines stochastic charge dynamics that incorporates the microscopically evaluated tunneling rates with a Newtonian dynamics. We have applied the multiscale model to describe the shuttling of a single copper atom between two gold-like jellium electrodes. We find that energy spectrum and particle surface interaction greatly influence shuttling dynamics; in the specific example that we studied the shuttling is found to involve only charge states Q=0 and Q=+e. The system is found to exhibit two quasi-stable shuttling modes, a fundamental one and an excited one with a larger amplitude of mechanical motion, with random transitions between them.Comment: 9 pages, 9 figure

Dynamical instabilities of a resonator driven by a superconducting single-electron transistor

We investigate the dynamical instabilities of a resonator coupled to a superconducting single-electron transistor (SSET) tuned to the Josephson quasiparticle (JQP) resonance. Starting from the quantum master equation of the system, we use a standard semiclassical approximation to derive a closed set of mean field equations which describe the average dynamics of the resonator and SSET charge. Using amplitude and phase coordinates for the resonator and assuming that the amplitude changes much more slowly than the phase, we explore the instabilities which arise in the resonator dynamics as a function of coupling to the SSET, detuning from the JQP resonance and the resonator frequency. We find that the locations (in parameter space) and sizes of the limit cycle states predicted by the mean field equations agree well with numerical solutions of the full master equation for sufficiently weak SSET-resonator coupling. The mean field equations also give a good qualitative description of the set of dynamical transitions in the resonator state that occur as the coupling is progressively increased.Comment: 23 pages, 6 Figures, Accepted for NJ