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. 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 nanomechanical devices, where the interplay between single-electron tunneling and a local mechanical degree of freedom significantly controls the electronic transport, is another line of nanoelectromechanics [6][7][8][9][10][11][12][13][14][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

An analytical analysis of quantum shuttle phenomena in a nanoelectromechanical single-electron transistor has been performed in the realistic case, when the electron tunneling length is much greater than the amplitude of the zero point oscillations of the central island. It is shown that when the dissipation is below a certain threshold value, the vibrational ground state of the central island is unstable. The steady state into which this instability develops is studied. It is found that if the electric field E between the leads is much greater than a characteristic value E(q), the quasiclassical shuttle picture is recovered, while if E<0) shuttle vibrations.

We consider effects of the spin degree of freedom on the nanomechanics of a single-electron transistor (SET) containing a nanometer-sized metallic cluster suspended between two magnetic leads. It is shown that in such a nanoelectromechanical SET (NEM-SET) the onset of an electromechanical instability leading to cluster vibrations and "shuttle" transport of electrons between the leads can be controlled by an external magnetic field. Different stable regimes of this spintronic NEM-SET operation are analyzed. Two different scenarios for the onset of shuttle vibrations are found.PACS numbers: 85.85.+j, 73.23.HK, 85.35.Be As the downsizing of electronic devices reaches the near molecular scale, the Coulomb forces associated with inhomogeneous charge distributions produced during device operation become comparable with the chemical forces that hold the device together. Consequently, the spatial configuration of a device may well change dynamically during its operation. This inherent feature of nanoelectronics can be turned into an advantage by designing the devices with the mechanical degrees of freedom in mind; this is the scope of nanoelectromechanics and the basis for nanoelectromechanical systems (NEMS) [1].A pronounced nanoelectromechanical phenomenonelectron transport by means of a nanoelectromechanical "shuttle" mechanism -has recently been predicted to occur in certain NEMS systems as a result of a bias voltage-induced nanoelectromechanical instability [2]. The most suitable device for the experimental observation of this phenomenon is a nanoelectromechanical single-electron transistor (NEM-SET). A NEM-SET is a single-electron transistor (SET) with a movable central island whose center-of-mass motion is confined by some potential. Experimental studies of NEM-SET devices can be found in Refs. [3,4,5]. They have also been extensively investigated theoretically [6,7,8,9,10].Another rapidly developing branch of condensed matter physics is spintronics [11], which deals with devices whose functionality depends on the control and manipulation of the spin rather than the charge of electrons. A recent development of great interest in this context is the demonstration of a magnetic hybrid nanostructure consisting of a single C 60 -molecule placed between two ferromagnetic electrodes [12]. The possibility to manipulate the spin of mechanically shuttled electrons in a molecular NEM-SET of this kind brings about an exciting opportunity to trigger nanomechanical vibrations in the THz range by means of a weak external magnetic * Present address: Kavli Institute of Nanoscience, TU Delft, Lorentzweg 1, 2628 CJ Delft, The Netherlands.field much smaller than the magnetic anisotropy fields in the leads. This Letter is devoted to exploring this very phenomenon. We will show that the spin-dependent tunneling of electrons between differently polarized leads results in a strong sensitivity to an external magnetic field of the nanoelectromechanical instability that is responsible for the shuttling. Depending on the magnitude of the...

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The voltage dependence of nanoelectromechanical effects in a system where the quantized mechanical vibrations of a quantum dot are coupled to coherent tunneling of electrons through a single level in the dot is studied. It is found that there are two different regimes depending on the value of an applied voltage. If the bias voltage is below a certain threshold value, then the state of the mechanical subsystem is located near its ground state. If the bias voltage is above the threshold value then the system becomes unstable which manifests itself in the expectation value of the displacement being an oscillating function of time with an exponentially increasing amplitude. This can be interpreted as a shuttle instability in a quantum regime.Nanoelectromechanical systems (NEMS), where electronic and mechanical degrees of freedom are coupled is a new and fast growing branch of condensed matter physics 1,2 . One such a system, a single-electron transistor (SET) where the conducting island has a vibrational degree of freedom associated with its center-of-mass motion (Fig.1), a so-called nanoelectromechanical-SET (NEM-SET), has been attracting a great deal of attention recently, both theoretically 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17 and experimentally 18,19 . PSfrag replacements x µL = eV 2 µR = − eV 2 Lead Lead Island FIG. 1: Model shuttle system consisting of a movable conducting island placed between two leads. An effective elastic force acting on the dot from the leads is described by the parabolic potential.In Ref. 3 it was shown, that the metallic grain placed between the two leads of NEM-SET becomes unstable and the periodic mechanical motion of the grain develops if a large bias voltage is applied between the leads. This phenomenon is usually referred to as a shuttle instability (see the review Ref. 20). A theory of the shuttle instability developed in Ref. 3 was based on the assumptions that both the charge on the island and its trajectory are well defined quantities.When we decrease the island size two different quantum effects manifest themself. Firstly, the electron energy level spacing in a nanometer-size grain is of the order of 10 K and resonant tunneling effects become essential at small enough temperatures. Therefore the single-electron energy spectrum can not be treated as continuous any more as it was done in Ref. 3. In this case the characteristic de Broglie wave length associated with the island can still be much shorter than the length scale of the spatial variations of the "mechanical" potential. If so, the motion of the island can be treated classically. This regime has been studied theoretically in Ref. 6.Diminishing the size of the island further (down to 7Å in diameter, for C 60 molecule) results in the quantization of the mechanical motion of the island. A NEM-SET system in the regime of quantized mechanical motion of the central island was studied theoretically in Ref. 5. It was assumed that the phase breaking processes are strong enough to make the density matrix diagonal in the represent...