  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 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 \textit{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 fixed number of
particles and in the strong coupling limit, the system still has an instability
to the normal sate with increasing hybridization.
