Dynamics of a nanoscale rotor driven by single-electron tunneling

We investigate theoretically the dynamics and the charge transport properties of a rod-shaped nanoscale rotor, which is driven by a similar mechanism as the nanomechanical single-electron transistor (NEMSET). We show that a static electric potential gradient can lead to self-excitation of oscillatory or continuous rotational motion. We identify the relevant parameters of the device and study the dependence of the dynamics on these parameters. We discuss how the dynamics are related to the measured current through the device. Notably, in the oscillatory regime we find a negative differential conductance. The current-voltage characteristics can be used to infer details of the surrounding environment which is responsible for damping. Copyright c © EPLA, 2012 Introduction. – In recent years it has emerged that the coupling of electrical and mechanical degrees of freedom on the nanometer scale provides the opportunity to build novel devices, extending the concepts of conventional electronic devices [1,2]. A seminal example is the nanomechanical single-electron transistor (NEMSET) [3–6], where electrons can tunnel from a source to a drain electrode via a movable island or grain, whose charge (i.e., the number of excess electrons that occupy the island) is determined by the Coulomb-blockade effect. Since the tunneling amplitude depends exponentially on the position of the island, the current is very sensitive to the mechanical motion. For a sufficiently large bias voltage a selfexcitation of periodic oscillations occurs in conjunction with charging and de-charging of the island. This mechanically assisted charge transport is called electron shuttling [3]. The grain is embedded in a medium which creates a restoring force and determines essentially the eigenfrequency of the oscillation of the shuttle. In this letter we consider a device which can rotate freely and which is driven by the same mechanism as the electron shuttle described above. The driving force is determined by a static voltage which is applied along the device [7–9]. In contrast to the conventional shuttles this results in a force that depends non-linearly on the relevant system coordinate. Moreover, there is no mechanical restoring (a)E-mail: [email protected] (b)E-mail: [email protected] force in the present case. The coupling of mechanical motion and tunneling leads, as we will show, to the selfexcitation of oscillatory and rotational motion even in the presence of damping. The frequency of oscillation (rotation) depends on the ratio of the driving force and the friction. While being based on the same principle as the charge shuttle, the present device exhibits noticeable differences. In the oscillatory regime, the current through the device decreases with increasing bias voltage, which is surprising from the conventional shuttling point of view. We attribute this effect to the presence of a separatrix in the phase space which separates oscillations from rotations. Approaching the separatrix involves a slowing-down of the dynamics and decreasing oscillation amplitudes, which results in the decreasing current. In the rotational regime, one may realize a nanoscale motor which is driven by a static voltage [9]. Using numerical calculations supplemented by an analytical analysis, we find that the dynamics of the rotor are governed by three dimensionless parameters, namely, tunneling length, field strength and damping constant. This circumstance allows us to predict, for example, a transition from oscillatory to rotational motion fairly independent of the actual realization (e.g., used materials, details of the shape) of the device. Our analysis provides an intuitive picture of the dynamics for a large range of the above parameters. For the specific case in which the rotor is based on the setup of fig. 1(a)