Spontaneous Time Reversal and Parity Breaking in adx2−y2-Wave Superconductor with Magnetic Impurities

Abstract

It is shown that patches of complex $d_{\mathrm{xy}}$ components are generated around a magnetic impurity in the presence of coupling between the orbital moment of the condensate and the impurity spin $S_z$. The locally induced $d_{\mathrm{xy}}$ gap leads to the fully gapped quasiparticle spectrum near impurity. It is suggested that at low temperatures the well defined patches of $d_{\mathrm{xy}}$ are formed, possibly leading to a phase locked state due to Josephson tunneling. Violation of time-reversal symmetry and parity occurs spontaneously at this point via a second order transition. In the ordered phase both the impurity magnetization and the $d_{\mathrm{xy}}$ component of the order parameter develop and are proportional to each other.