Self-Oscillating Josephson Quantum Heat Engine

The design of a mesoscopic self-oscillating heat engine that works thanks to purely quantum effects is presented. The proposed scheme is amenable to experimental implementation with current state-of-the-art nanotechnology and materials. One of the main features of the structure is its versatility: The engine can deliver work to a generic load without galvanic contact. This versatility makes it a promising building block for low-temperature on-chip energy-management applications. The heat engine consists of a circuit featuring a thermoelectric element based on a ferromagnetic insulator-superconductor tunnel junction and a Josephson weak link that realizes a purely quantum dc-ac converter. This makeup enables the contactless transfer of work to the load (a generic RL circuit). The performance of the heat engine is investigated as a function of the thermal gradient applied to the thermoelectric junction. Power up to 1 pW can be delivered to a load $R_L=10\mathrm{\Omega }$.

Figure 1

(a) Scheme of the Josephson quantum heat engine. (b) Thermodynamic scheme. The heat current generates a dc electric current, which is (partly) converted into an ac signal by the Josephson junction. A corresponding ac current is induced to the load circuit by electromagnetic coupling. (c) Equivalent electric circuit. The symbols and the voltage convections used in the text are indicated.

Figure 2

Density plot of zero-voltage thermoelectric current provided by the $N\text{−}\mathrm{FI}\text{−}S$ element. Parameters are $P=0.9$, $T_{C0}=3.0\mathrm{K}$, $R_T=0.1\mathrm{\Omega }$, $\mathrm{\Gamma }={10}^{-4}{\mathrm{\Delta }}_0$, and $h_{\mathrm{exc}}=0.4{\mathrm{\Delta }}_0$, where ${\mathrm{\Delta }}_0=1.764k_B{T}_{C0}$ and $T_{C0}$ is the zero-field critical temperature. In the black region, $|I_{TE}^0|<3\mu \mathrm{A}$. The contour lines for $|I_{TE}^0|=10\mu \mathrm{A}$ ($A$) and $|I_{TE}^0|=100\mu \mathrm{A}$ ($B$) are plotted in white.

Figure 3

Transmitted power vs thermal gradient for (top panels) $I_c=10\mu \mathrm{A}$ and (bottom panels) $I_c=100\mu \mathrm{A}$. (Left panels) Numerical data are compared to (right panels) the expression Eq. (9). The regions where Eq. (9) gives a higher estimate than the largest value of $\overline{\mathcal{P}}$ in the corresponding numerical graph are drawn in gray. The stars denote the points investigated in Fig. 4. Parameters are $C=100\mathrm{fF}$, $L_1=L_2=100\mathrm{pH}$, $M=10\mathrm{pH}$, $R_S=1\mathrm{\Omega }$, and $R_L=10\mathrm{\Omega }$.

Figure 4

Transmitted power vs load resistance for different working points in the $(T_S,T_N)$ space, marked by the stars in Fig. 3. Numerical data (the solid lines) are compared with the expression Eq. (9) (the dashed lines). Parameters are $C=100\mathrm{fF}$, $L_1=L_2=100\mathrm{pH}$, $M=10\mathrm{pH}$, $R_S=1\mathrm{\Omega }$, and $I_c=100\mu \mathrm{A}$.