Fluctuations in a superconducting quantum critical point of multi-band metals

In multi-band metals quasi-particles arising from different atomic orbitals coexist at a common Fermi surface. Superconductivity in these materials may appear due to interactions within a band (intra-band) or among the distinct metallic bands (inter-band). Here we consider the suppression of superconductivity in the intra-band case due to hybridization. The fluctuations at the superconducting quantum critical point (SQCP) are obtained by calculating the response of the system to a fictitious space- and time-dependent field, which couples to the superconducting order parameter. The appearance of superconductivity is related to the divergence of a generalized susceptibility. For a single-band superconductor this coincides with the Thouless criterion. For fixed chemical potential and large hybridization, the superconducting state has many features in common with breached pair superconductivity with unpaired electrons at the Fermi surface. The T = 0 phase transition from the superconductor to the normal state is in the universality class of the density-driven Bose-Einstein condensation. For a fixed number of particles and in the strong coupling limit, the system still has an instability to the normal state with increasing hybridization.