Large thermoelectric effect in ballistic Andreev interferometers

TL;DR

This paper demonstrates a large thermoelectric effect in ballistic NS hybrid structures caused by electron-hole asymmetry from Andreev reflection, with a general expression for thermoelectric voltages derived.

Contribution

It introduces a theoretical model that explains the thermoelectric effect in multiterminal ballistic NS structures and derives a general formula for thermoelectric voltages under thermal gradients.

Findings

Thermoelectric voltages depend on temperature and phase differences.

No fundamental relation exists between thermoelectric voltages and Josephson current.

Results are valid at any temperature difference in the subgap regime.

Abstract

Employing quasiclassical theory of superconductivity combined with Keldysh technique we investigate large thermoelectric effect in multiterminal ballistic normal-superconducting (NS) hybrid structures. We argue that this effect is caused by electron-hole asymmetry generated by coherent Andreev reflection of quasiparticles at interfaces of two different superconductors with non-zero phase difference. Within our model we derive a general expression for thermoelectric voltages $V_{T1,2}$ induced in two different normal terminals exposed to a thermal gradient. Our results apply at any temperature difference in the subgap regime and allow to explicitly analyze both temperature and phase dependencies of $V_{T1,2}$ demonstrating that in general there exists no fundamental relation between these voltages and the equilibrium Josephson current in SNS junctions.