Quantum Theory of Magnetoelectromotive Instability in Nanoelectromechanical Systems with Positive Differential Conductance

We consider dc-electronic transport through a nanowire suspended between two normal-metal leads in the presence of an external magnetic field. We show the very mechanism through which such a system, whose stationary current-voltage characteristic is essentially characterized by positive differential conductance, becomes unstable with respect to an onset of self-excited oscillations in electrical transport and mechanical vibrations. The self-excitation mechanism is based on the correlation between the occupancy of the quantized spin-split electronic energy levels inside the nanowire and the velocity of the nanowire with the crucial influence of strong enough retardation effects in magnetomotive coupling coming from mechanical vibrations.

Figure 1

(a) A nanowire subjected to an external magnetic field $\mathbf{B}$, suspended between two normal-metal leads biased symmetrically by voltages $\pm V_b$. (b) Electronic energy scheme for the junction: ${\epsilon }_{\uparrow ,\downarrow }$ are spin-split levels in the nanowire, and $\mu$ is the chemical potential in the leads without bias. The junction is nonsymmetric in the sense that the tunneling barrier between $D$ and nanowire is thicker than between $S$ and nanowire. (c) A stationary current-voltage characteristic of the junction always exhibiting essentially positive differential conductance ($V_{\uparrow ,\downarrow }\equiv {\epsilon }_{\uparrow ,\downarrow }/e$).

Figure 2

(a) The “dynamical potential” $\kappa (E)/D$ whose zero point $E_c$ determines the maximum of the Wigner function $W(E)$ describing the probability of finding a mechanical system at a certain energy $E$ (dimensionless units). (b) Density plot of the probability $W(u,p)$ in mechanical ($u$, $p$) phase space, indicating the existence of a classical limit cycle at its maximum measured from the static equilibrium state determined by $u_0$. The used parameters are $\lambda =0.1$, $\gamma =0.1$, $\Omega =0.3$, $\beta =0.95$, and $\eta =3.5\times {10}^{-5}$ ($Q=8.6\times {10}^4$).