Surface effects in magnetic superconductors with a spiral magnetic structure

TL;DR

This paper investigates how boundary conditions affect the Green's functions in magnetic superconductors with spiral magnetic structures, revealing oscillatory corrections and their impact on Josephson current calculations.

Contribution

It introduces a boundary-sensitive analysis of Green's functions in spiral magnetic superconductors, showing significant deviations from bulk-based calculations of Josephson current.

Findings

Boundary conditions cause oscillations in Green's functions with period 2π/Q.

Corrections decay over a length scale related to temperature and material properties.

Critical Josephson current differs notably from bulk-based estimates.

Abstract

We consider a magnetic superconductor MS with a spiral magnetic structure. On the basis of generalized Eilenberger and Usadel equations we show that near the boundary of the MS with an insulator or vacuum the condensate (Gor'kov's) Green's functions are disturbed by boundary conditions and differ essentially from their values in the bulk. Corrections to the bulk quasiclassical Green's functions oscillate with the period of the magnetic spiral, $2\pi /Q$, and decay inside the superconductor over a length of the order $v/\pi T$ (ballistic limit) or $\sqrt{D/\pi T}$ (diffusive limit). We calculate the dc Josephson current in an MS/I/MS tunnel junction and show that the critical Josephson current differs substantially from that obtained with the help of the tunnel Hamiltonian method and bulk Green's functions.