Patterns of coexisting superconducting and particle-hole condensates

We have studied systematically the influence of particle-hole symmetric and asymmetric kinetic terms on the ordered phases that we may observe competing or coexisting in a tetragonal system. We show that there are precise patterns of triplets of ordered phases that are accessible (i.e. it is impossible to observe two of them without the third one). We found a systematic way to predict these patterns of states and tested it by identifying at least 16 different patterns of three order parameters that necessarily coexist in the presence of the kinetic terms. We show that there are two types of general equations governing the competition of all these triplets of order parameters and we provide them.