Field induced $d_{x^2-y^2}+id_{xy}$ state and marginal stability of high-Tc superconductors

TL;DR

The paper demonstrates that magnetic fields induce a complex $d_{x^2-y^2}+i d_{xy}$ order parameter in high-Tc superconductors, leading to a parity- and time-reversal-violating state with a small but finite $id_{xy}$ component.

Contribution

It reveals the mechanism by which magnetic fields generate a complex order parameter component, causing a novel superconducting state with broken symmetries.

Findings

Magnetic field induces a complex $d_{x^2-y^2}+i d_{xy}$ state.

Transition occurs into a state violating P and T symmetries.

The $id_{xy}$ component magnitude is estimated to be a few Kelvin.

Abstract

It is shown that the {\em complex} $d_{xy}$ component is generated in d-wave superconductor in the magnetic field. As one enters superconducting state at finite field the normal to superconducting transition occurs into bulk $d_{x^2-y^2}+i d_{xy}$ state . The driving force for the transition is the linear coupling between magnetic field and non zero magnetization of the $d_{x^2-y^2}+i d_{xy}$ condensate. The external magnetic field violates parity and time reversal symmetries and the nodal quasiparticle states respond by generating the $id_{xy}$ component of the order parameter, with the magnitude estimated to be on the order of few Kelvin. Parity (P) and time reversal (T) symmetries are violated in this state.