Magnetic impurity induced id_{xy} component and spontaneous time reversal and parity breaking in a d_{x^2-y^2}-wave superconductor

TL;DR

This paper investigates how magnetic impurities induce a complex d_{xy} component in a d_{x^2-y^2} superconductor, leading to spontaneous time-reversal and parity breaking through a phase transition.

Contribution

It demonstrates the formation of localized d_{xy} patches around impurities and their role in spontaneous symmetry breaking in a superconductor.

Findings

Localized d_{xy} patches form around impurities.

Spontaneous time-reversal symmetry breaking occurs at low temperatures.

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

Abstract

It is shown that the patches of complex d_{xy} component are generated around magnetic impurity in the presence of the coupling between orbital moment of the condensate and impurity spin S. Locally induced d_{xy} gap leads to the fully gapped quasiparticle spectrum near impurity. The phase of the induced i d_{xy} component is determined by impurity spin and averages to zero at high temperatures. It is suggested that at low temperature the well defined patches of d_{xy} are formed and they can undergo a phase transition into phase locked state via Josephson effect. 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.