Theory of proximity effect in $s+p$-wave superconductor junctions

TL;DR

This paper develops a theoretical framework for understanding the proximity effect in diffusive normal metal / $s+p$-wave superconductor junctions, revealing how dominant pairing symmetry influences local density of states and conductance, with implications for spin-triplet superconductivity.

Contribution

It derives a boundary condition for Green's functions in mixed parity superconductor junctions and applies it to analyze LDOS and conductance in an $s+p$-wave model.

Findings

LDOS shows a gap-like structure when s-wave dominates

Zero energy peak appears when p-wave dominates

Quantized conductance is robust for dominant p-wave pairing

Abstract

We derive a boundary condition for the Nambu Keldysh Green's function in diffusive normal metal / unconventional superconductor junctions applicable for mixed parity pairing. Applying this theory to a 1d model of $s+p$-wave superconductor, we calculate LDOS in DN and charge conductance of DN / $s+p$-wave superconductor junctions. When the $s$-wave component of the pair potential is dominant, LDOS has a gap like structure at zero energy and the dominant pairing in DN is even-frequency spin-singlet $s$-wave. On the other hand, when the $p$-wave component is dominant, the resulting LDOS has a zero energy peak and the dominant pairing in DN is odd-frequency spin-triplet $s$-wave. We show the robustness of the quantization of the conductance when the magnitude of $p$-wave component of the pair potential is larger than that of $s$-wave one. These results show the robustness of the anomalous proximity effect specific to spin-triplet superconductor junctions.