Superconducting nonlinear thermoelectric heat engine

Abstract

In a previous work, we predicted that a thermally biased tunnel junction between two different superconductors can display a thermoelectric effect of nonlinear nature in the temperature gradient, under proper conditions. In this work we give a more extended discussion, and we focus on the two main features of the nonlinear contributions: i) the linear-in-bias thermoelectricity, that can be associated to a spontaneous breaking of electron-hole symmetry, ii) the strong contribution at the matching peak singularity, which is typically associated to the maximum output power and efficiency. We discuss the nonlinear origin of the thermoelectricity and its relationship with the non-linear cooling mechanism in superconducting junctions previously discussed in the literature. Finally, we design and characterize the performance of the system as a heat engine, for a realistic design and experimental parameter values. We discuss possible non-idealities demonstrating that the system is amenable to current experimental realization.

Spontaneous symmetry breaking-induced thermospin effect in superconducting tunnel junctions

“…We can note the dissipative behavior [I q (V )/V > 0] around V ∼ 0 and thermoelectricity [I q (V )/V < 0] around ±V − p . This difference between linear and nonlinear in bias behavior has been reported also in absence of h exc for nonlinear thermoelectric systems [39]. For a more complete discussion, we show also the spin current for the same values.…”

“…This condition results in the following inequality for the charge current, I q (δV, δT ) = −I q (−δV, δT ) [36,37]. This limitation can be overcome in the presence of a large temperature bias (nonlinear regime), as recently demonstrated in tunnel junctions between superconductors with different energy gaps [38,39]. Here, we investigate the thermo-spin effect induced by spontaneous PH symmetry breaking in hybrid ferromagnetic insulator/superconductor systems for a large temperature bias.…”

“…For a fixed h exc , thermoelectricity is present only in a limited range of T L . In particular, the maximum value of T L providing a thermoelectric effect is due to the condition ∆(T L ) > ∆(T R ) − h exc (dashed white line), which corresponds to the requirement to have the hot electrode with the largest "effective" gap [38,39]. We now consider thermoelectricity at internal peak voltages…”

“…This quantity plays a crucial role when the thermoelectric element is connected to a load. More precisely, −G max represents the maximal conductance of the load supported by the thermoelectric junction, such as no net thermopower can be generated if the load conductance is bigger than −G max [39]. Figure 2(d) shows G max as a function of h exc and T L .…”

Temperature-biased double-loop Josephson flux transducer

“…Surprisingly, the critical current can even increase with the temperature, thus suggesting to apply this phenomenon for a wide-band threshold calorimeter [12]. Furthermore, strong nonlinear temperature biases can induce a spontaneous breaking of the particle-hole symmetry, generating even a bypolar thermoelectric effect [14,15].…”