Odd-frequency pairing in a superconductor coupled to two parallel nanowires

TL;DR

This paper investigates how odd-frequency pairing arises in a superconductor coupled to two nanowires, revealing its impact on local density of states and Josephson current, and how it can be controlled experimentally.

Contribution

It demonstrates the conversion of non-local odd-frequency pairing to local even-frequency pairing in a superconductor-nanowire system without spin-orbit coupling or magnetism.

Findings

Odd-frequency pairing induces subgap features in the local density of states.

Odd-frequency pairing reduces the maximum Josephson current between nanowires.

Strong tunneling enables symmetry conversion from odd-frequency to even-frequency pairing.

Abstract

We study the behavior of Cooper pair amplitudes that emerge when a two-dimensional superconductor is coupled to two parallel nanowires, focusing on the conditions for realizing odd-frequency pair amplitudes in the absence of spin-orbit coupling or magnetism. In general, any finite tunneling between the superconductor and the two nanowires induces odd-frequency spin-singlet pair amplitudes in the substrate as well as a substantial odd-frequency interwire pairing, both of which vanish locally. Interestingly, in the regime of strong superconductor-nanowire tunneling, we find that the presence of two nanowires allows for the conversion of non-local odd-frequency pairing to local even-frequency pairing. By studying this higher-order symmetry conversion process, we are able to identify a notable effect of the odd-frequency pairing in the superconductor on local quantities accessible by experiments. Specifically, we find that the odd-frequency pairing plays a direct role in the emergence of certain subgap features in the local density of states, and, importantly, it is responsible for a reduction of the maximum Josephson current between the two nanowires, measurable using Josephson scanning tunneling microscopy. We discuss ways to control the sizes of these effects induced by odd-frequency superconductivity by tuning the parameters describing the nanowires.