Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of the spin-orbit coupling

TL;DR

This paper extends the quasiclassical Green's function formalism to describe magnetoelectric effects and triplet correlations in superconducting heterostructures with spin-orbit coupling, revealing new mechanisms for triplet pairing without magnetic fields.

Contribution

It introduces a generalized quasiclassical theory valid for weak spin-orbit coupling that enables quantitative analysis of magnetoelectric effects and triplet correlations in hybrid superconducting systems.

Findings

Triplet correlations can be induced without magnetic fields.

Triplet correlations contain an odd-frequency component.

The theory predicts a proportionality to the ratio of spin-orbit coupling to Fermi energy.

Abstract

The quasiclassical theory in terms of equations for the Green's functions (Eilenberger equations) is generalized in order to allow for quantitative description of the magneto-electric effects and proximity-induced triplet correlations in the presence of spin-orbit coupling in hybrid superconducting systems. The formalism is valid under the condition that the spin-orbit coupling is weak with respect to the Fermi energy, but exceeds the superconducting energy scale considerably. On the basis of the derived formalism it is shown that the triplet correlations in the spin-orbit coupled normal metal can be induced by proximity to a singlet superconductor without any exchange or external magnetic field. They contain an odd-frequency even-momentum component, which is stable against disorder. The value of the proximity-induced triplet correlations is of the order of $\Delta_{so}/\varepsilon_F$, that is absent in the framework of the standard quasiclassical approximation, but can be described by our theory. The spin polarization, induced by the Josephson current flowing through the superconductor/Rashba metal/superconductor junction, is also calculated.