Quantum transport through a rigidly connected double quantum-dot shuttle

We design a double quantum-dot (QD) shuttle (DQDS) model including two rigidly connected QDs that are softly linked to two leads via deformable organic materials. Based on the full quantum mechanical approaches we explore the influences on the electron transport induced by the electrical and mechanical degrees of freedom. First of all the modified rate equations of the DQDS are derived theoretically and then a numerical investigation on the quantum transport through the DQDS is performed. For the classical DQDS, the time-dependent evolutions of the electron-occupation probabilities and the currents flowing through the DQDS show the periodic oscillations with their periods determined by the oscillation period of the DQDS. Both the mechanical oscillation amplitude and the interdot coupling can play crucial roles in adjusting the peak shapes of the currents and the probabilities. For the quantum DQDS, the current and electron-occupation probabilities of the DQDS evolve into a stationary state as time goes on, with no periodical oscillations observed. As a consequence, the sharp differences of the time-dependent properties between the classical and quantum DQDS systems are clearly demonstrated, which should be greatly helpful in designing new nanoelectromechanical devices. Also, this work is of great significance to understanding the kind of rigidly connected QD shuttle systems that have more than two QDs.