Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling

TL;DR

This paper analytically investigates how Rashba spin-orbit coupling in nanowire junctions induces both even- and odd-frequency superconducting pair correlations, revealing the mechanisms and spatial behaviors of these correlations.

Contribution

It demonstrates the universal presence of odd-frequency pairing in Rashba nanowire junctions and elucidates the processes generating different pairing symmetries using a quantum scattering approach.

Findings

Odd-frequency pairing is induced by Andreev reflection at interfaces.

Odd-frequency components dominate at low frequencies in NS junctions.

In short SNS junctions, odd-frequency correlations dominate at $\, ext{ extbackslash pi}$-phase difference.

Abstract

We consider normal-superconductor (NS) and superconductor-normal-superconductor (SNS) junctions based on one-dimensional nanowires with Rashba spin-orbit coupling and proximity-induced $s$-wave spin-singlet superconductivity and analytically demonstrate how both even- and odd-frequency and spin-singlet and -triplet superconducting pair correlations are always present. In particular, by using a fully quantum mechanical scattering approach, we show that Andreev reflection induces mixing of spatial parities at interfaces, thus being the unique process which generates odd-frequency pairing; on the other hand, both Andreev and normal reflections contribute to even-frequency pairing. We further find that locally neither odd-frequency nor spin-triplet correlations are induced, but only even-frequency spin-singlet pairing. In the superconducting regions of NS junctions, the interface-induced amplitudes decay into the bulk, with the odd-frequency components being generally much larger than the even-frequency components at low frequencies. The odd-frequency pairing also develops short and long-period oscillations due to the chemical potential and spin-orbit coupling, respectively, leading to a visible beating feature in their magnitudes. Moreover, we find that in short SNS junctions at $\pi$-phase difference and strong spin-orbit coupling, the odd-frequency spin-singlet and -triplet correlations strongly dominate with an alternating spatial pattern for a large range of sub-gap frequencies.