Spin injection and spin relaxation in odd-frequency superconductors

TL;DR

This paper investigates spin transport and relaxation in odd-frequency superconductors, revealing enhanced spin injection, temperature-dependent density of states transitions, and significant spin-orbit scattering effects near the gap edge.

Contribution

It introduces a theoretical framework for spin transport in odd-frequency superconductors and uncovers unique spin injection and relaxation phenomena not seen in conventional superconductors.

Findings

Enhanced spin injection due to density of states properties

Temperature-induced transition from gapless to gapped states

Significant reduction in spin-orbit scattering time near the gap edge

Abstract

The spin transport inside an odd-frequency spin-triplet superconductor differs from that of a conventional superconductor due to its distinct symmetry properties. We study spin transport inside an emergent odd-frequency superconductor by replacing the spin-singlet gap matrix in the Usadel equation with a matrix representing spin-triplet pairing that is odd under inversion of energy. We show that the peculiar nature of the density of states allows for an even larger spin injection than in the normal-state. Moreover, when the odd-frequency pairing inherits its temperature dependence from a conventional superconductor through the proximity effect, the density of states can transition from gapless to gapped as the temperature decreases. At the transition point, the spin accumulation inside the odd-frequency superconductor is peaked and larger than in the normal-state. While the spin-flip scattering time is known to decrease below the superconducting transition temperature in conventional superconductors, we find that the same is true for the spin-orbit scattering time in odd-frequency superconductors. This renormalization is particularly large for energies close to the gap edge, if such a gap is present.