Fluctuation-induced first-order transitions in unconventional superconductors

Abstract

Generalized Ginzburg-Landau models of complex-vector order parameters are investigated by the mean-field approximation and the renormalization-group theory. Mean-field results for the possible ordered phases and their domains of stability are presented. The availability of large regions on the phase diagram in which the phase transitions are of first order is established. The fixed points of the renormalization-group equations and their stability properties are investigated up to second order in \ensuremath{\epsilon}=4-d. Except for systems with cubic anisotropy, the renormalization-group equations do not have stable fixed points, and this indicates the presence of fluctuation-driven first-order transitions. For cubic symmetries a new critical behavior is reported. The results are related to superconductivity in high-${\mathit{T}}_{\mathit{c}}$ oxides and heavy-fermion systems.