Abstract
The strong coupling between electronic transport in a single-level quantum dot and a capacitively coupled nano-mechanical oscillator may lead to a transition towards a mechanically-bistable and blocked-current state. Its observation is at reach in carbon-nanotube state-of-art experiments. In a recent publication [Phys. Rev. Lett. 115, 206802 (2015)] we have shown that this transition is characterized by pronounced signatures on the oscillator mechanical properties: the susceptibility, the displacement fluctuation spectrum and the ring-down time. These properties are extracted from transport measurements, however the relation between the mechanical quantities and the electronic signal is not always straightforward. Moreover the dependence of the same quantities on temperature, bias or gate voltage, and external dissipation has not been studied. The purpose of this paper is to fill this gap and provide a detailed description of the transition. Specifically we find: (i) The relation between the current-noise and the displacement spectrum. (ii) The peculiar behavior of the gate-voltage dependence of these spectra at the transition. (iii) The robustness of the transition towards the effect of external fluctuations and dissipation.
Highlights
Electronic transport allows for detection of the displacement of extremely small mechanical oscillators, like carbon nanotubes.[9]
Strong coupling can lead to an unexpected behavior of the system, as it was first recognized in studying coherent electronic transport in molecular junctions coupled to low-frequency vibrations.[10,11]
II we introduce the microscopic model describing a singlelevel quantum dot coupled to a mechanical oscillator, we present a Langevin and Fokker-Planck description of the system dynamics
Summary
Detection and actuation of mechanical systems at the nano-scale is a present-day challenge that has important fundamental and application perspectives.[1,2,3,4,5,6,7,8] Electronic transport allows for detection of the displacement of extremely small mechanical oscillators, like carbon nanotubes.[9]. In a very recent publication we investigated some of the features expected when the transition is studied varying the coupling constant P at low temperature (ω0 V, T P ).[38] we found that the mechanical mode softens at the transition to the bistable state, with a minimal value controlled by the bias voltage, and that phase fluctuations dominate the dynamics leading to a universal quality factor of 1.71. This provided a first glance on the transition scenario, but several points deserve to be investigated in order to clarify the full picture.
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