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, dx2−y2, and dxy channels). Various consequences of the subdominant channels (i.e., s and dxy channels) are examined in detail. (1) In the case of a dx2−y2+is-wave superconductor, we reproduce an earlier result that there is a second-order zero-field transition from the pure dx2−y2 phase to the time-reversal-symmetry– (T-) breaking dx2−y2+is-phase at the temperature TDS. The structure of a single vortex above and below TDS is fourfold and twofold symmetric, respectively. (2) In the case of a dx2−y2+idxy-wave superconductor, there is also a second-order zero-field phase transition from the pure dx2−y2 phase to the T-breaking dx2−y2+idxy-wave phase at the temperature TDD′. In contrast to the case in a dx2−y2+is-wave superconductor, the subdominant phase cannot be induced by vortices above TDD′. 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 dx2−y2 and dxy waves is found to have significant effects on the low-temperature behavior of dx2−y2+idxy superconductors. In a magnetic field, a dx2−y2+idxy state is always established, but the field dependence of dxy amplitude above TDD′ is different from that below TDD′. Above but not very close to TDD′, the induced minimum gap Δ0∝B/(T−TDD′).

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