Peltier effects in Andreev interferometers

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.