Quantum transport through a transverse quantum-dot shuttle

A transverse quantum-dot (QD) shuttle (T-QDS) is proposed where the QD oscillating direction is perpendicular to the electron transmission direction, different from the usual QD shuttle where the oscillating direction is parallel to the electron transmission direction. Both the electrical and mechanical degrees of freedom are dealt with by using the full quantum mechanical approaches. We derive the modified rate equations and numerically investigate the quantum properties of the T-QDS. First, as a comparison, we study the time-dependent evolutions of the electron-occupation probabilities and the currents flowing through the classical T-QDS. It is shown that the current shows the time-dependent oscillation in phase with the oscillation of the T-QDS. Then, we turn to study the quantum properties of the quantum T-QDS. Sharply different from the classical T-QDS, no oscillations of the probabilities and the current are observed due to the quantum uncertainty of the space position of the quantum T-QDS. It is demonstrated that the effects induced by the quantized oscillation of the quantum T-QDS are reflected as the renormalization of the tunneling rates between the QD and the leads. Notably, the two tunneling rates of the QD with the left and right leads depend on the relative space positions of the leads and the QD in different ways. It is the interplay of the two tunneling rates that eventually determines the stationary current of the T-QDS. Moreover, we study the influences induced by the temperature, which can also be considered via the renormalized tunneling rates.