Effects of phase coherence on local density of states in superconducting proximity structures

We theoretically study the local density of states in superconducting proximity structures where two superconducting terminals are attached to a side surface of a normal-metal wire. Using the quasiclassical Green's function method, the energy spectrum is obtained for both spin-singlet s-wave and spin-triplet p-wave junctions. In both cases, the decay length of the proximity effect at zero temperature is limited by a depairing effect due to inelastic scattering. In addition to the depairing effect, in p-wave junctions the decay length depends sensitively on the transparency at the junction interfaces, which is a unique property of odd-parity superconductors where the anomalous proximity effect occurs.