We develop a general framework for describing thermoelectric effects in phase-coherent superconducting structures. Formulas for the electrical conductance, thermal conductance, thermopower, and Peltier coefficient are obtained and their various symmetries discussed. Numerical results for both dirty and clean Andreev interferometers are presented. We predict that giant oscillations of the thermal conductance can occur, even when oscillations in the electrical conductance are negligibly small. Results for clean, two-dimensional systems with a single superconducting inclusion are also presented, which show that normal-state oscillations arising from quasiparticle boundary scattering are suppressed by the onset of superconductivity. In contrast, for a clean system with no normal-state boundary scattering, switching on superconductivity induces oscillations in off-diagonal thermoelectric coefficients.

We present a comprehensive theory of lhe elecrrical conductance C of phase-coherent, multi-channel. resonant sbllclures in lhe presence of superconductivay. When voltages of the order of the level spacing are applied, pmticle-hole symmetry is broken and our results differ significantly from earlier descriptions. After deriving generafizations of the well-known Breit-Wigner formula, valid in the presence of superconductivity, results for resonant transport in ulree classes of sbllchlre are obtained. First. for a superconducting dol (SDOT) connected to n o d contacts (N). we examine the change in conductance as the magnitude of L e superconducting order parameter increases from zero. W e change is typically negative, except near a normalslate resonance. where large positive changes can occur. Secondly, for a struchut comprising a normal (N) contacl, a normal dot (NDOT) and a superconducting (S) contact, we predict that finite-voltage. differential conductance resonances are strongly suppressed by the switching on of superconductivity in the S contact. In the weak-mupling limit, resonances which survive have a double-&ed line-shape. Thirdly, analytic results a n presented for superconductivityenhanced. quasi-particle inrerferometers (SEQUINS). which demonsme lhat resonant SEQUINS can provide galvanomeaic magnetic flux detectors, with a sensitivity in excess of the flux quantum.

We examine transport properties of superconducting hybrid mesoscopic structures, in both the diffusive and ballistic regimes. For diffusive structures, analytic results from quasi-classical theory are compared with predictions from numerical, multiple-scattering calculations performed on small structures. For all structures, the two methods yield comparable results and in some cases, quantitative agreement is obtained. These results not only demonstrate that quasi-classical theory can yield the ensemble averaged conductance < G > of small structures of dimensions of order 10-20 Fermi wavelengths, but also establish that numerical scattering calculations on such small structures can yield results for < G > which are characteristic of much larger systems. Having compared the two approaches, we extend the multiple-scattering analysis to the ballistic limit, where the sample dimensions become smaller than the elastic mean free path and demonstrate that the properties of certain Andreev interferometers are unchanged in the clean limit.

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