Time reversal symmetry breaking superconductivity

Abstract

We study time reversal symmetry breaking superconductivity with $Δ_k = Δ_{x^2-y^2} (k) +e^{iθ} Δ_α$ ($α= s$ or $d_{xy}$) symmetries. It is shown that the behavior of such superconductors could be {\em qualitatively} different depending on the minor components ($α$) and its phase at lower temperatures. It is argued that such {\em qualitatively different} behaviors in thermal as well as in angular dependencies could be a {\em source} of consequences in transport and Josephson physics. Orthorhombicity is found to be a strong mechanism for mixed phase (in case of $α= s$). We show that due to electron correlation the order parameter is more like a pure $d_{x^2-y^2}$ symmetry near optimum doping.