Spontaneous time reversal and parity breaking in a $d_{x^2-y^2}$-wave superconductor with magnetic impurities

TL;DR

This paper explores how magnetic impurities induce a spontaneous transition in a $d_{x^2-y^2}$ superconductor to a state that breaks time-reversal symmetry and parity, leading to a mixed order parameter phase.

Contribution

It demonstrates that magnetic impurities can cause a spontaneous $d_{x^2-y^2} + id_{xy}$ transition, revealing a new mechanism for symmetry breaking in unconventional superconductors.

Findings

Transition to $d_{x^2-y^2} + id_{xy}$ state occurs with magnetic impurities.

Impurity magnetization and $d_{xy}$ component are proportional in the ordered phase.

Time-reversal symmetry and parity are spontaneously broken in this transition.

Abstract

It is argued that the $d_{x^2-y^2}$ superconductor exhibits the transition into $d_{x^2-y^2} + id_{xy}$ state in the presence of magnetic impurities in certain conditions. Linear coupling between impurity magnetization and the $d_{xy}$ component drives this transition. Violation of time-reversal symmetry and parity occurs spontaneously via the second order transition. In the ordered phase both impurity magnetization and $d_{xy}$ component of the order parameter develop and are proportional to each other.