Nanoelectromechanical Heat Engine Based on Electron-Electron Interaction

We theoretically show that a nanoelectromechanical system can be mechanically actuated by a heat flow through it via an electron-electron interaction. In contrast to most known actuation mechanisms in similar systems, this new mechanism does not involve an electronic current nor external ac fields. Instead, the mechanism relies on deflection-dependent tunneling rates and a heat flow which is mediated by an electron-electron interaction while an electronic current through the device is prohibited by, for instance, a spin-valve effect. Therefore, the system resembles a nanoelectromechanical heat engine. We derive a criterion for the mechanical instability and estimate the amplitude of the resulting self-sustained oscillations. Estimations show that the suggested phenomenon can be studied using available experimental techniques.

Figure 1

The prototype system. A CNT is suspended between two leads, below a tip electrode and above a gate. The pair of leads and the tip are two completely spin-polarized electron reservoirs with temperatures $T_{\uparrow }$ and $T_{\downarrow }$ (index according to spin polarization). Electrons can tunnel between the CNT and the reservoirs, but an electron exchange between the two reservoirs is prevented by spin blockade. However, electron-electron interaction couples the two reservoirs, allowing for a heat flow. The tunneling between the tip and the CNT is affected by $u$, the mechanical deflection of the CNT (black arrow), and $u$ is in turn affected by a capacitive force due to the interaction between the charge on the CNT and the gate.

Figure 2

Schematic energy diagram of the electronic states of the QD and the tunneling processes (dotted arrows). The average flows of probability between the different states are illustrated by the solid arrows $w_{\alpha }^{\sigma }$. The average flow is counterclockwise, since only electrons from the hot electron have enough energy to overcome the electron-electron interaction energy and bring the QD to the double-populated state.

Figure 3

The intrinsic mechanical damping (dashed line) and heat-flow-induced pumping (solid lines), given by the first and second term, respectively, in the rhs of Eq. (10). If the pumping overcomes the damping, the system is actuated to an amplitude where the two are balanced (line intersections). We use parameters as in Table 1 and ${\mathrm{\Gamma }}_{\sigma }=\omega /2$, $E_1^{\sigma }=-U/2$ ($\sigma =\uparrow ,\downarrow$), which are the optimal values for pumping, and $Q=3\times 10^4$. The pumping is shown for different temperatures $T_{\uparrow }$ of the hot reservoir, while the cold reservoir is kept at $T_{\downarrow }=0.1\mathrm{K}$.