Analysis of collective excitation for multi band superconductor: Frustrated spin model approach

•We study properties of multi-band superconductors.•The multi-band system can be mapped into a frustrated spin system.•Time-reversal symmetry is broken due to the frustration.•The mass of the Leggett mode vanishes in certain parameter region.

We study properties of multi-band superconductors, focusing on their ground states and collective excitations. Multi-band tight-binding Hamiltonian with repulsive pair-hopping interaction is mapped into a frustrated spin-Hamiltonian. This frustration leads to exotic features in a multi-band superconductor.Applying the mean-field theory to the three- and four-band systems, we systematically examine the superconducting-phase structure between multiple order parameters, and the associated collective modes.