Marginal stability of d-wave superconductor: spontaneous P and T violation in the presence of magnetic impurities

We argue that the $d_{x^2-y^2}$-wave superconductor is marginally stable in the presence of external perturbations. Subjected to the external perturbations by magnetic impurities, it develops a secondary component of the gap, complex $d_{xy}$, to maximize the coupling to impurities and lower the total energy. The secondary $d_{xy}$ component exists at high temperatures and produces the full gap $\sim 20 K$ in the single particle spectrum around each impurity, apart from impurity induced broadening. At low temperatures the phase ordering transition into global $ d_{x^2-y^2} + i d_{xy}$ state occurs.