Microscopically derived multi-component Ginzburg-Landau theories for $s+is$ superconducting state

Starting with the generic Ginzburg-Landau expansion from a microscopic $N$-band model, we focus on the case of a 3-band model which was suggested to be relevant to describe some iron-based superconductors. This can lead to the so-called $s+is$ superconducting state that breaks time-reversal symmetry due to the competition between different pairing channels. Of particular interest in that context, is the case of an interband dominated pairing with repulsion between different bands. For that case we consider in detail the relevant reduced two-component Ginzburg-Landau theory. We provide detailed analysis of the ground state, length scales and topological properties of that model.