Peltier effects in Andreev interferometers

TL;DR

This paper investigates how the superconducting proximity effect influences the Peltier effect in Andreev interferometers, revealing a significant enhancement due to nonequilibrium supercurrents carrying energy.

Contribution

It analyzes symmetry relations between thermoelectric coefficients and calculates the Peltier effect in hybrid structures, highlighting the impact of phase differences on thermoelectric transport.

Findings

Proximity effect enhances Peltier effect in superconducting hybrids.

Finite phase differences lead to larger Peltier coefficients.

Supercurrents carry energy, affecting thermoelectric properties.

Abstract

The superconducting proximity effect is known to modify transport properties of hybrid normal--superconducting structures. In addition to changing electrical and thermal transport separately, it alters the thermoelectric effects. Changes to one off-diagonal element $L_{12}$ of the thermoelectric matrix $L$ have previously been studied via the thermopower, but the remaining coefficient $L_{21}$ which is responsible for the Peltier effect has received less attention. We discuss symmetry relations between $L_{21}$ and $L_{12}$ in addition to the Onsager reciprocity, and calculate Peltier coefficients for a specific structure. Similarly as for the thermopower, for finite phase differences of the superconducting order parameter, the proximity effect creates a Peltier effect significantly larger than the one present in purely normal-metal structures. This results from the fact that a nonequilibrium supercurrent carries energy.