Spin-Controlled Nanomechanics Induced by Single-Electron Tunneling

We consider dc-electronic transport through a nanowire suspended between normal- and spin-polarized metal leads in the presence of an external magnetic field. We show that magnetomotive coupling between the electrical current through the nanowire and vibrations of the wire may result in self-excitation of mechanical vibrations. The self-excitation mechanism is based on correlations between the occupancy of the quantized electronic energy levels inside the nanowire and the velocity of the nanowire. We derive conditions for the occurrence of the instability and find stable regimes of mechanical oscillations.

Figure 1

(a) A carbon nanotube (CNT) subject to an external magnetic field $H$, suspended between normal (n) and magnetic (m) metal leads biased by voltages $\pm V_b$. (b) Electronic energy scheme for the junction: $\mu$ is the chemical potential, ${\epsilon }_{\uparrow ,\downarrow }$ are spin-split levels in the CNT, ${\epsilon }_k^{(n)}$ and ${\epsilon }_{k\sigma }^{(m)}$ are electron energy bands in the leads ($k$ is the wave vector, $\sigma$ is spin).

Figure 2

Behavior of the function $\Phi (A)$ defined in Eq. (7) for different magnetic fields leading to (a) soft excitation of nanowire oscillations at $\Delta V\equiv V_b-({ϵ}_0-\mu )/e=0.34\mathrm{mV}$ and (b) hard excitation at $\Delta V=0.41\mathrm{mV}$. Other parameter values are $T=0.2\mathrm{K}$, $Q=3\times {10}^4$, ${\Gamma }_D^{\downarrow }/{\Gamma }_S=0.4$, $\omega /{\Gamma }_S=0.2$

Figure 3

(a) Stability diagram for nanowire oscillations in the ($H$, $\Delta V$) plane, where $\Delta V=V_b-({ϵ}_0-\mu )/e$. In the white and dark gray regions there is only one stable stationary state corresponding to a nonmoving and a vibrating nanowire, respectively. The light gray region is where both these states are stable. (b) Average current in units of $e{\Gamma }_S$, in (b-1) as a function of bias voltage $\Delta V$ for $H=10\mathrm{T}$ [horizontal line in (a)] and in (b-2) as a function of magnetic field $H$ for $\Delta V=0.4\mathrm{mV}$ [vertical line in (a)]. The full (dashed) lines show the result for an ascending (descending) magnetic field. The gray dotted curves correspond to a static nanowire. Other parameters: $T=0.2\mathrm{K}$, $Q=3\times {10}^4$, ${\Gamma }_D^{\downarrow }/{\Gamma }_S=0.4$, $\omega /{\Gamma }_S=0.1$.