Subdominant pairing channels in unconventional superconductors: Ginzburg-Landau theory

Abstract

A Ginzburg-Landau theory is developed for unconventional superconductors with the three relevant singlet pairing channels (i.e., s, d x2- y2, and d xy channels). Various consequences of the subdominant channels (i.e., s and d xy channels) are examined in detail. (1) In the case of a d x2- y2+is-wave superconductor, we reproduce an earlier result that there is a second-order zero-field transition from the pure d x2- y2 phase to the time-reversal-symmetry- (T-) breaking d x2- y2+is-phase at the temperature T DS. The structure of a single vortex above and below T DS is fourfold and twofold symmetric, respectively. (2) In the case of a d x2- y2+id xy-wave superconductor, there is also a second-order zero-field phase transition from the pure d x2- y2 phase to the T-breaking d x2- y2+id xy-wave phase at the temperature T DD′. In contrast to the case in a d x2- y2+is-wave superconductor, the subdominant phase cannot be induced by vortices above T DD′. Below the T-breaking transition, the subdominant phase in the mixed state is nontrivial: it survives at low fields, but may disappear above a field (increasing with decreasing temperature) presumably via a first-order transition. (3) By including the strong-coupling effects, a T-breaking-coupling term between the d x2- y2 and d xy waves is found to have significant effects on the low-temperature behavior of d x2- y2+id xy superconductors. In a magnetic field, a d x2- y2+id xy state is always established, but the field dependence of d xy amplitude above T DD′ is different from that below T DD′. Above but not very close to T DD′, the induced minimum gap Δ 0∝B/(T-T DD′). ©1999 The American Physical Society.