Viscous AC current-driven nanomotors

Abstract

The recent discovery that electrons in nano-scale conductors can act like a highly viscous liquid has triggered a surge of research activities investigating consequences of this surprising fact. Here we demonstrate that the electronic viscosity has an enormous influence on the operation of a prototypical AC-current-driven nano-motor. The design of this prototype consists of a diatomic molecule immersed in an otherwise homogeneous electron liquid which carries an AC current. The motion of the diatomic is determined by a subtle balance between the current-induced forces and electronic friction. By ab-initio time-dependent density-functional simulations we demonstrate that the diatomic performs a continuous rotation provided the amplitude and frequency of the imposed AC current lie within certain islands of stability. Outside these islands the nuclear motion is either chaotic or comes to a stand-still. The proposed design of the nano-motor is the conceptually simplest realization of the idea of an molecular waterwheel sandwiched between conducting leads

Figures (7)

• Figure 1: Angle between the instantaneous direction of the axis of the impurity $\mathbf{R}_r(t)$ and its initial value $\mathbf{R}_r(0)$ versus time. Starting from $t=0$, the current density $\bar{\mathbf{j}}(t)=\bar{\mathbf{j}}_0 \sin \omega t$ is applied with $\bar{\mathbf{j}}_0$ perpendicular to $\mathbf{R}_r(0)$ and $|\bar{\mathbf{j}}_0|= 4 \times 10^{-5}$ a.u. At selected current frequencies, exemplified by $\omega=0.70 \times 10^{-4}$ and $0.55 \times 10^{-4}$ a.u., a continuous rotation of the impurity (the wavy straight lines in the graph) takes place, while it is suppressed for $\omega= 0.73\times 10^{-4}$ and $0.53\times 10^{-4}$ a.u. Inset shows separately, on a magnified scale, the same time evolution for $\omega=0.53 \times 10^{-4}$ a.u., where rotation stalled at the angle of $-90^\circ$ is observed.
• Figure 2: Phase-diagram, in the current density amplitude -- frequency coordinates, for HEG of $r_s=2$ a.u. Within the painted areas (bands), a continuous rotation persists, while it is forbidden outside of it.
• Figure 3: Same as Fig. \ref{['ggrs2']}, but $r_s=6$ a.u. The lower panel shows the phase diagram with neglect of the viscosity contribution [${\rm Im} \, f_{xc}(q,\omega)$ set to zero].
• Figure 4: Same as Fig. \ref{['ggrs6']}, but $r_s=10$ a.u.
• Figure 5: Angle of rotation of the molecule versus time. Results of the full calculations by Eqs. \ref{['vcr14']}-\ref{['vcr24']} are compared with those of the pendulum model of Eqs. \ref{['pend1']}-\ref{['pend4']}.