Non-linear dynamics of a driven nanomechanical single electron transistor

Published in Physical Review B, 2013

P. G. Kirton and A. D. Armour Phys. Rev. B 87, 155407 (2013)

We analyze the response of a nanomechanical resonator to an external drive when it is also coupled to a single-electron transistor (SET). The interaction between the SET electrons and the mechanical resonator depends on the amplitude of the mechanical motion leading to a strongly nonlinear response to the drive which is similar to that of a Duffing oscillator. We show that the average dynamics of the resonator is well described by a simple effective model which incorporates damping and frequency renormalization terms which are amplitude dependent. We also find that for a certain range of parameters the system displays interesting bistable dynamics in which noise arising from charge fluctuations causes the resonator to switch slowly between different dynamical states.