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

## TL;DR

This paper investigates how phase coherence influences the local density of states in superconducting proximity structures, highlighting differences between s-wave and p-wave junctions and the effects of interface transparency.

## Contribution

It provides a theoretical analysis of the energy spectrum in superconducting proximity structures with both s-wave and p-wave pairing, emphasizing the role of interface transparency and depairing effects.

## Key findings

- Decay length limited by inelastic scattering at zero temperature
- Decay length in p-wave junctions depends on interface transparency
- Anomalous proximity effect occurs in odd-parity superconductors

## Abstract

We theoretically study the local density of states in superconducting proximity structure 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 of spin-singlet $s$-wave and spin-triplet $p$-wave junctions. In both of the cases, the decay length of the proximity effect at the zero temperature is limited by a depairing effect due to inelastic scatterings. 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 to odd-parity superconductors where the anomalous proximity effect occurs.