Powerful Coulomb-drag thermoelectric engine

We investigate a thermoelectric nanoengine whose properties are steered by Coulomb interaction. The device whose design decouples charge and energy currents is made up of two interacting quantum dots connected to three different reservoirs. We show that, by tailoring the tunnel couplings, this setup can be made very attractive for energy-harvesting prospects, due to a delivered power that can be of the order of the quantum bound [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014); Entropy 18, 208 (2016)], with a concomitant fair efficiency. To unveil its properties beyond the sequential quantum master equation, we apply a nonequilibrium noncrossing approximation in the Keldysh Green's function formalism, and a quantum master equation that includes cotunneling processes. Both approaches are rather qualitatively similar in a large operating regime where sequential tunneling alone fails.

Figure 1

Schematic representation of the device and of currents of interest: The top dot is connected to a hot reservoir and coupled by Coulomb interaction to a second dot (bottom). The latter is connected to two cold reservoirs through which a bias voltage can be applied. The energy current $J_t^E$ flows from the top dot, while the electric current $J_b^e$ flows through the bottom one.

Figure 2

Comparison between the NCA and the QME with (seq + cot) and without (seq) cotunneling processes: The output power $\mathcal{P}$, in ${\mathrm{\Gamma }}^2/\hslash$ units, is displayed as a function of bias voltage, for $U=10T_h,{\epsilon }_d=-U/2,\mathrm{\Gamma }=T_h/100,T_c=0.2T_h$ (solid lines), or $T_c=0.6T_h$ (dashed lines).

Figure 3

Top panel: Charge current in $e\mathrm{\Gamma }/\hslash$ units, evaluated in the QME and in the NCA, for $U=6\mathrm{\Gamma },T_h=\mathrm{\Gamma }$, and $T_c=0.2T_h$. The renormalized energy current evaluated in the NCA, $\frac{e{J}_t^E}{U}$, is also presented. Bottom: Green's functions for the same parameters, and for $V$ equal to the upper panel stopping voltage.

Figure 4

NCA calculations for the same parameters as in Fig. 3: $U=6\mathrm{\Gamma },{\epsilon }_d=-U/2,T_h=\mathrm{\Gamma }$, and $T_c=0.2T_h$. The hybridization functions are shifted by $\delta$. Top panel: electric current in $e\mathrm{\Gamma }/\hslash$ units, middle panel: ratio of device to Carnot efficiencies as a function of bias, bottom: ratio of device to Carnot efficiencies as a function of renormalized power. See text for details.