Transport via a quantum shuttle

Abstract

We investigate the effect of a quantized vibrational mode on electron tunneling through a chain of three quantum dots. The outer dots are coupled to voltage leads, but the position of the central dot is not rigidly fixed. Motion of the central dot modulates the size of the tunneling barriers in opposite ways so that electron tunneling is correlated with the position of the oscillator. We treat the electronic part of the problem using a simple Coulomb-blockade picture, and model the vibration of the central dot as a quantum oscillator. We calculate the eigenspectrum of the system as a function of the energy level shift between the outer dots. Using a density matrix method, we include couplings to external leads and calculate the steady-state current through the device. The current shows marked resonances that correspond to avoided-level crossings in the eigenvalue spectrum. When the tunneling length of the electrons is of order the zero-point position uncertainty of the quantum oscillator, current far from the electronic resonance is dominated by electrons hopping on and off the central dot sequentially; the oscillator can be regarded as shuttling electrons across the system ͓L.Y. Gorelik et al., Phys. Rev. Lett. 80, 4526 ͑1998͔͒. Damping of the oscillator can increase the current by preventing electrons from hopping ''backwards.''

Semiclassical dynamics of nanoelectromechanical systems

“…This has turned out to be a highly successful approach, in particular to describe such various systems as NEMS coupled to single electron transistors (SETS) [9][10][11] , FranckCondon blockades 12 in transport through molecules with strong electron-phonon coupling, or quantum shuttles [13][14][15][16] . From the theory of electronic transport through nanostructures 17 , however, it is known that such approximations usually are reliable only in the limit of high external voltage bias, where non-Markovian effects 18 due to quantum coherences between the external reservoirs and the electronic system (SET, quantum dot etc.)…”

Current and current fluctuations in quantum shuttles

“…͑1a͒. 4,23,31 The leads are held at different electrochemical potentials L,R whose difference gives the bias across the array ͓see Fig. 1͔.…”

Impact of van der Waals forces on the classical shuttle instability

“…Experimental shuttle related work has been reported on cantilevers that work as flexible tunneling contacts [7,8,9], singlemolecule transistors [10], colloidal particle systems [11], and macroscopic shuttle systems [12]. Theoretical work has included different aspects of classical shuttle systems [6,13,14,15,16], some noise and accuracy considerations [17,18], different aspects of quantum mechanical shuttle models [19,20,21,22,23,24], and shuttling of Cooper pairs in a superconducting shuttle system [25,26]. For a recent review, see Ref.…”