Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures

TL;DR

This paper classifies pairing correlations in superconductor-ferromagnet nanostructures based on symmetry, revealing how inhomogeneity and interface effects induce various pairing components, including long-range odd-frequency correlations.

Contribution

It provides a comprehensive symmetry classification of pairing correlations near superconductor-ferromagnet interfaces, highlighting the role of spin-active scattering and inhomogeneity in inducing diverse pairing states.

Findings

Inhomogeneity causes mixing of even- and odd-energy pairing components.

Spin-active interfaces induce all symmetry components, including long-range odd-frequency correlations.

Universal temperature dependence of the Josephson critical current in tunneling limit.

Abstract

Using selection rules imposed by the Pauli principle, we classify pairing correlations according to their symmetry properties with respect to spin, momentum, and energy. We observe that inhomogeneity always leads to mixing of even- and odd-energy pairing components. We investigate the superconducting pairing correlations present near interfaces between superconductors and ferromagnets, with focus on clean systems consisting of singlet superconductors and either weak or half-metallic ferromagnets. Spin-active scattering in the interface region induces all of the possible symmetry components. In particular, the long-range equal-spin pairing correlations have odd-frequency s-wave and even-frequency p-wave components of comparable magnitudes. We also analyze the Josephson current through a half-metal. We find analytic expressions and an interesting universality in the temperature dependence of the critical current in the tunneling limit.