Ginzburg-Landau energy of multiband superconductors with interband pairing

We derive microscopically the Ginzburg-Landau free-energy functional for a superconductor in which the Cooper pairs are formed not only by quasiparticles from the same band, but also by quasiparticles from different bands. In the simplest case of an s- or d-wave pairing in a two-band system, the order parameter has three components describing two intraband and one interband pair condensates. The interband pairing-specific terms in the free energy bring about some qualitative features in the phase diagram, for example, time-reversal symmetry-breaking superconducting states are stabilized at low temperatures. We also show that, despite the fact that the gradient energy of the interband component turns negative at a sufficiently large band splitting, a nonuniform superconducting instability is generally suppressed due to the hybridization of the intraband and interband condensates.