Vibrational Instability Due to Coherent Tunneling of Elec- Trons


PACS. 73.63.-b – Electronic transport in mesoscopic or nanoscale materials and structures.. PACS. 73.23.Hk – Coulomb blockade; single-electron tunneling. PACS. 85.85.+j – Micro-and nano-electromechanical systems (MEMS/NEMS) and devices. Abstract. – Effects of a coupling between the mechanical vibrations of a quantum dot placed between the two leads of a single electron transistor and coherent tunneling of electrons through a single level in the dot has been studied. We have found that for bias voltages exceeding a certain critical value a dynamical instability occurs and mechanical vibrations of the dot develop into a stable limit cycle. The current-voltage characteristics for such a transistor were calculated and they seem to be in a reasonably good agreement with recent experimental results for the single C60-molecule transistor by Park et al. Introduction. – Nanoelectromechanics [1, 2] is a new, quickly developing field in condensed matter physics. A coupling between strongly pronounced mesoscopic features of the electronic degrees of freedom (such as quantum coherence and quantum correlations) and degrees of freedom connected to deformations of the material produces strong electromechanical effects on the nanometer scale. The mesoscopic force oscillations in nanowires [3–5] observed a few years ago is an example of such a phenomenon. Investigations of artificially-made nanome-chanical devices, where the interplay between single-electron tunneling and a local mechanical degree of freedom significantly controls the electronic transport, is another line of nanoelec-tromechanics [6–15]. For one of the nanomechanical systems of this kind, the self-assembled single-electron transistor, a new electromechanical phenomena-the shuttle instability and a new so-called shuttle mechanism of the charge transport were recently predicted in [12]. It was shown that a small metallic grain attached to two metallic electrodes by elastically deformable links breaks into oscillations if a large enough bias voltage is applied between the leads. For the model system studied in [12], it was also shown that a finite friction is required for the oscillation amplitude to saturate and for a stable regime of oscillations to develop. An essential assumption made in [12] is that the relaxation mechanisms present are strong enough to keep the electron systems in each of the conducting parts of the transistor in local equilibrium (as assumed in the standard theory of Coulomb blockade [16,17]). Such relaxation, which destroys any phase coherence between electron tunneling events, allows a description of

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