Abstract
In spite of extended efforts, detecting thermoelectric effects in superconductors has proven to be a challenging task, due to the inherent superconducting particle-hole symmetry. Here we present a theoretical study of an experimentally attainable Superconductor – Quantum Dot – Superconductor (SC-QD-SC) Josephson Junction. Using Keldysh Green’s functions we derive the exact thermo-phase and thermal response of the junction, and demonstrate that such a junction has highly tunable thermoelectric properties and a significant thermal response. The origin of these effects is the QD energy level placed between the SCs, which breaks particle-hole symmetry in a gradual manner, allowing, in the presence of a temperature gradient, for gate controlled appearance of a superconducting thermo-phase. This thermo-phase increases up to a maximal value of ±π/2 after which thermovoltage is expected to develop. Our calculations are performed in realistic parameter regimes, and we suggest an experimental setup which could be used to verify our predictions.
Highlights
To overcome the absence of current, experiments in which the setup comprises a bi-metallic loop, were proposed and performed[11,12]
Control over its magnitude can be achieved by a gate voltage, which shifts the energy levels of the quantum dot (QD), allowing for breaking of the p-h symmetry even for ideal SC electrodes, enabling experimental control of the magnitude and direction of the thermal response
The usefulness of this form for the current stems from the fact that within the relevant parameter range discussed here, the phase dependence of the amplitude of the various current terms is negligible. This phase dependence originates from multiple reflections between the QD and the leads, giving rise to higher harmonic processes with a non trivial phase function. These reflections diminish as a function of Γs/ε, i.e. as the energy level in the QD moves away from the Fermi level, and as a result Cooper pairs have smaller probability of tunneling across the junction
Summary
To overcome the absence of current, experiments in which the setup comprises a bi-metallic loop (taking advantage of the fact that the SC phase has to be geometrically quantized), were proposed and performed[11,12]. Suggestions for increasing the thermal response and p-h asymmetry include using magnetic impurities[17] or a ferromagnetic junction setup[18], leading to a thermo-phase of greater magnitude. Using a magnetic field for tuning the system parameters[19] leads to substantial experimental limitations. Control over its magnitude can be achieved by a gate voltage, which shifts the energy levels of the QD, allowing for breaking of the p-h symmetry even for ideal SC electrodes, enabling experimental control of the magnitude and direction of the thermal response. Our model consists of bulk s-type superconductors as leads, with individual gap energies and arbitrary phases (taken symmetrically for convenience), and a single QD level in between.
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