Stochastic model of nanomechanical electron shuttles and symmetry breaking

Nanomechanical electron shuttles can work as ratchets for radio-frequency rectification. We develop a full stochastic model of coupled shuttles, where the mechanical motion of nanopillars and the incoherent electronic tunneling are modeled by a Markov chain. In particular, the interaction of their randomness is taken into account, so that a linear master equation is constructed. Numerical solutions from our fast approximate method and analytical derivation reveal the symmetry breaking, which results in the direct current observed in earlier measurements [Phys. Rev. Lett. 105, 067204 (2010)]. Additionally, the method can facilitate device simulation of more complex designs such as shuttle arrays.

Figure 1

(a) Coupled nanomechanical electron shuttles, set with electrodes S, D and optionally G1, G2, oscillate under driving voltage and have electrons tunneled. (b) Side view of a typical design where shuttles are on top of nanopillars.

Figure 2

Direct current versus driving frequency (with an offset of the average eigenfrequency of the two shuttles 500 MHz), when driving amplitude is 1 V and a second-order harmonic with amplitude of 0.5 V introduces asymmetry. The difference of two eigenfrequencies are varied for three curves, indicated in the legend.

Figure 3

Peak direct current (over the frequency) versus driving voltage amplitude $V_1$, with different ratios of second-order amplitude $V_2/V_1$.