We consider a nanoelectromechanical Josephson junction, where a suspended nanowire serves as a superconducting weak link, and show that an applied dc bias voltage can result in suppression of the flexural vibrations of the wire. This cooling effect is achieved through the transfer of vibronic energy quanta first to voltage-driven Andreev states and then to extended quasiparticle electronic states. Our analysis, which is performed for a nanowire in the form of a metallic carbon nanotube and in the framework of the density matrix formalism, shows that such self-cooling is possible down to the ground state of the flexural vibration mode of the nanowire.

We investigate theoretically the dynamics of a spatially symmetric shuttle system subjected to an ac gate voltage. We demonstrate that in such a system parametric excitation gives rise to mechanical vibrations when the frequency of the ac signal is close to the eigenfrequency of the mechanical subsystem. These mechanical oscillations result in a dc shuttle current in a certain direction due to spontaneous symmetry breaking. The direction of the current is determined by the phase shift between the ac gate voltage and the parametrically excited mechanical oscillations. The dependence of the shuttle current on the dc gate voltage is also analyzed. Some years ago, a novel form of electron transport-a shuttle mechanism-based on the mechanical vibrations of a metallic nanoparticle coupled to two electrodes via elastic molecular links was proposed in Ref. 1. Since then, the shuttle phenomenon has been a subject of intensive experimental and theoretical research. [2][3][4][5][6][7] The main feature of the orthodox shuttle phenomenon is that a constant potential difference, applied between two fixed electrodes, leads to a dynamical instability that causes the metal nanoparticle to oscillate. As a consequence, a dc current through the system, induced by the voltage drop between the electrodes, becomes proportional to the frequency of the mechanical oscillations 1 . The idea of shuttle phenomena was also extended to the quantum realm [8][9][10][11] . Nanoelectromechanical shuttle systems have been also studied in the regime of ac excitation and several interesting effects on the transport properties and the dynamics of the shuttle system have been found [12][13][14][15][16] . In particular, a shuttle structure driven by a time-dependent bias voltage has been considered in Refs. 17 and 18. It was shown that in case of asymmetric configuration such a setup can act as a rectifier, where the intensity of the dc current depends on the ratio between the frequency of the external oscillating voltage and the eigenfrequency of the mechanical subsystem. Current rectification was also conjectured by Ahn et al. 19 (and experimentally verified by Kim et al. 20 ) for the case of a symmetric double-shuttle structure. They attributed current-rectification phenomena to spontaneous symmetry breaking in the system caused by parametric instability. One of the conclusions of this work is that dynamical symmetry breaking in single shuttle systems does not lead to a dc current. Parametric excitation of nanoelectromechanical systems (NEMS) has been also considered in Refs. 21-23.In the present work, we investigate the possibility to generate a shuttle dc current, rather than rectifying current, in a completely symmetric single-dot shuttle system. We demonstrate that, in this scheme, despite the lack of a bias voltage, a shuttle dc current can still be detected. This charge transport is achieved by applying an ac voltage to a gate electrode which controls the electronic population of a metallic island and, in this form, also the stiffness of the...

We consider a new type of cooling mechanism for a suspended nanowire acting as a weak link between two superconductive electrodes. By applying a bias voltage over the system, we show that the system can be viewed as a refrigerator for the nanomechanical vibrations, where energy is continuously transferred from the vibrational degrees of freedom to the extended quasiparticle states in the leads through the periodic modulation of the inter-Andreev level separation. The necessary coupling between the electronic and mechanical degrees of freedom responsible for this energy-transfer can be achieved both with an external magnetic or electrical field, and is shown to lead to an effective cooling of the vibrating nanowire. Using realistic parameters for a suspended nanowire in the form of a metallic carbon nanotube we analyze the evolution of the density matrix and demonstrate the possibility to cool the system down to a stationary vibron population of ∼ 0.1. Furthermore, it is shown that the stationary occupancy of the vibrational modes of the nanowire can be directly probed from the DC current responsible for carrying away the absorbed energy from the vibrating nanowire. PACS numbers: 73.23.-b Electronic transport in mesoscopic systems; 74.45.+c Proximity effects; Andreev reflection; SN and SNS junctions; 85.85.+j Micro-and nano-electromechanical systems (MEMS/NEMS) and devices.

We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak-link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement present different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic and chaotic. Transitions between these regimes are also discussed.