Equal contribution of even and odd frequency pairing to transport across normal metal-superconductor junctions

TL;DR

This paper demonstrates that odd-frequency pairing is a universal feature in the current across normal metal-superconductor junctions, regardless of the pairing symmetry, using analytical and numerical methods based on the Green function approach.

Contribution

It reveals that equal contributions of even and odd frequency pairing are generic in NS junctions, providing a new perspective on interpreting transport phenomena in hybrid superconducting structures.

Findings

Odd-frequency pairing is ubiquitously present in NS junctions.

Equal contribution of even and odd frequency pairing in Andreev reflection.

Analysis applies to various pairing symmetries like s-wave, p-wave, d-wave.

Abstract

Odd-frequency pairing is an unconventional type of Cooper pairing in superconductors related to the frequency dependence of the corresponding anomalous Green function. We show by a combination of analytical and numerical methods that odd-frequency pairing is ubiquitously present in the current of Andreev-scattered particles across a junction formed by a normal metal (N) and a superconductor (S), even if the superconducting pairing is of conventional $s$-wave, spin singlet type. We carefully analyze the conductance of NS junctions with different pairing symmetries ($s$-wave, $p$-wave, $d$-wave). In all cases, we identify a generic equal balance of even and odd frequency pairing to the contributions related to Andreev reflection. This analysis shows in retrospect that the presence of odd-frequency pairing in electric currents across NS junctions is rather the rule, not the exception. This insight stems from an alternative approach of analyzing the transport problem of hybrid structures. It is based on the Kubo-Greenwood formula with direct access to symmetries of the anomalous Green functions characterizing the superconducting pairing. We expect that our predictions substantially enrich the interpretation of transport data across NS junctions in many material combinations.