BCS-BEC crossover in a two-band superconductor: A $GG_0$ $T$-matrix approach*

In view of recent exciting results in experiments on FeSe multi-band superconductors, we theoretically investigate the effects of pairing fluctuation in a two-band superconductor where both intra- and inter-band pairing interactions are taken into account. Our approach is based on a diagrammatic self-consistent $T$-matrix method with a $GG_0$ pair propagator. We will discuss the implications of the matrix structure of the pair propagator on the Thouless criterion and the form of self-energies. To understand experimental results on the size of the pseudogap, we specifically focus on the interplay between the strength of intra-band pairing interaction and the size of the pseudogap region when one of the two bands is in the BCS-BEC crossover regime. To offer research directions for future experiments and confirm the nature of pseudogap in a two-band superconductor, we also compute several other important physical quantities including density-density response functions, critical temperature, and fermionic chemical potential as functions of temperature and the strengths of intra- and inter-band interactions.