Current patterns and magnetic impurities in time-reversal breaking superconductor

TL;DR

This paper investigates how impurities affect time-reversal symmetry breaking superconductors, revealing spontaneous currents and impurity-induced phenomena through numerical analysis of different pairing symmetries.

Contribution

It provides a numerical study of impurity effects in ${ m T}$-violating superconductors, highlighting the induced currents and magnetic impurity effects, especially in p-wave systems.

Findings

Impurity induces spontaneous currents reflecting Cooper pair structures.

Magnetic impurities cause zero-energy level crossings in p-wave superconductors.

Current patterns vary with different ${ m T}$-violating pairing symmetries.

Abstract

We study the impurity effect in the time reversal symmetry (${\cal T}$) breaking superconductor based on the Bogoliubov-de Gennes (BdG) equations. In ${\cal T}$-violating superconductors, spontaneous currents are induced around the impurity. The current patterns around the impurity reflect the structures of the Cooper pairs. We investigate impurity problem numerically for two kinds of ${\cal T}$ violating superconductors $(p_{x}\pm {\rm i}p_{y}$ and $d+{\rm i}s)$ and investigate the currents around the impurity. We also study the effects of the magnetic impurity in p-wave ($p_{x}\pm {\rm i}p_{y}$) superconductor, especially in view of the zero-energy crossing of energy levels related to the phase transition of the ground state.