Spontaneously Symmetry-Broken Current in Coupled Nanomechanical Shuttles

We investigate the transport and the dynamical properties of tunnel-coupled double charge shuttles. The oscillation frequencies of two shuttles are mode-locked to integer multiples of the applied voltage frequency $\omega$. We show that left/right-symmetric double shuttles may generate direct net current due to bistable motions caused by parametric instability. The symmetry-broken direct current appears near $\omega =\Omega_{0}/(2j-1)$, ($j=1,2,...$), where $\Omega_{0}$ is the dressed resonance frequency of the relative motion of the two shuttles.