Mechanical Resonator Linearly Coupled to a Normal State Single Electron Transistor and Electron Transport in Mescoscopic Conductor

Abstract

We have studied the coupling of normal state single electron transistor and electron transport  in mesoscopic conductor. For this we have used a simple model system consisting of a  mechanical resonator linearly coupled to a normal state single electron transistor to explore  the nonlinear dynamics which arised in non electromechanical systems. We have found that  very weak linear electromechanical coupling gave rise to a strongly nonlinear response when  the resonator was driven close to resonance. In the weak coupling limit and in the absence of  driving, the single electron transistor acts on the resonator like a thermal bath with an  effective temperature proportional to the bias voltage; it also damps the mechanical motion  and renormalized the frequency of the resonator. We have found that for drive a certain  threshold, the mechanical response as a function of frequency becomes strongly nonlinear  and the mechanical system displayed many of the characteristics of the Duffing oscillator,  frequency pulling, a strongly asymmetric line shape, hystresis and bistability. The  electromechanical coupling was found weak. We have described the effect of the single  electron transistor on the resonator in terms of simple model which included damping and  frequency renormalization terms which are both amplitude dependent. We have found that a  calculation of the average mechanical response as a function of drive frequency using these  two quantities leaded to results which were found in good agreement with a Monte Carlo  simulation of the coupled dynamics. At large amplitudes the effect of the resonator on the  single electron transistor charge dynamics can no longer be accounted for by a linear  correction to the tunnel rates and the charge transport was strongly modified. The modified  charge dynamics loaded to changes in the damping and frequency shift induced by the single  electron transistor on the resonator leading in general to an amplitude dependence of these  quantities. Such amplitude dependence is generic in non linear oscillators and leaded to the  familiar phenomena of asymmetric frequency response hystresis and bistability. The obtained  results were found in good agreement with previously obtained results.