Long-range thermoelectric effects in mesoscopic superconductor-normal metal structures

We consider a mesoscopic four-terminal superconductor-normal metal structure in the presence of a temperature gradient along the N wire. A thermoemf arises in this system even in the absence of the thermoelectric quasiparticle current if the phase difference between the superconductors is not zero. We show that the thermoemf is not small in the case of a negligible Josephson coupling between two superconductors. It is also shown that the thermoelectric voltage has two maxima: one at a low temperature and another at a temperature close to the critical temperature. The obtained temperature dependence of the thermoemf describes qualitatively experimental data.