Impact of van der Waals forces on the classical shuttle instability

Abstract

The effects of including the van der Waals interaction in the modelling of the single electron shuttle have been investigated numerically. It is demonstrated that the relative strength of the vdW-forces and the elastic restoring forces determine the characteristics of the shuttle instability. In the case of weak elastic forces and low voltages the grain is trapped close to one lead, and this trapping can be overcome by Coulomb forces by applying a bias voltage V larger than a threshold voltage Vu. This allows for grain motion leading to an increase in current by several orders of magnitude above the transition voltage Vu. Associated with the process is also hysteresis in the I-V characteristics.

Low-frequency current noise of the single-electron shuttle

“…Although, as explained in [13], the non-parabolic confining potential smoothens any step-structure in the current-voltage characteristics, the transition between static-and shuttle-operation is clearly visible in the noise spectrum. Below the threshold voltage the Fano factor is of the order 1/2 whereas in the shuttle regime, it is higher.…”

“…For the elastic force we use a phenomenological non-linear potential [13] acting as a harmonic well with spring force constant k for small displacements but that diverges as a Lennard-Jones potential (12th power) at the positions X L and X R : 13 , where…”

“…Since current through the system is accompanied by charging of the grain, interplay between the Coulomb forces and the mechanical degrees of freedom can lead to self-oscillations of the grain, which in turn, supports charge transport through shuttling of electrons between the leads. Much work, both experimental [5,6,7,8,9] as well as theoretical [4,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] has been reported in this field.…”

Quantum transport through a transverse quantum-dot shuttle

“…On the other hand, the renormalized tunneling rates can be expressed by tracing in the position representation |q as L =¯ L Tr osc [L 2 (y)σ th (0)] =¯ L dq q|L 2 (y)σ th (0)|q =¯ L dq L 2 (q)P th (q) (16) and R =¯ R Tr osc [R 2 (y)σ th (eE)]=¯ R dq q|R 2 (y+d)σ th (0)|q…”

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][28][29][30] For example, Novotný et al 29,30 present a quantum theory of the shuttle instability in electronic transport through such a NEMS with a horizontal oscillation degree of freedom and observe a clear crossover from the tunneling to the shuttling regime of the transport as a function of the mechanical damping parameter. As a counterpart where the horizonal oscillation is completely frozen and only the transverse oscillation is taken into account, what will happen in this regime is still an open question.…”