  In fermionic systems with different types of quasi-particles, attractive
interactions can give rise to exotic superconducting states, as pair density
wave (PDW) superconductivity and breached pairing. In the last years the search
for these new types of ground states in cold atom and in metallic systems has
been intense. In the case of metals the different quasi-particles may be the up
and down spin bands in an external magnetic field or bands arising from
distinct atomic orbitals that coexist at a common Fermi surface. These systems
present a complex phase diagram as a function of the difference between the
Fermi wave-vectors of the different bands. This can be controlled by external
means, varying the density in the two-component cold atom system or, in a
metal, by applying an external magnetic field or pressure. Here we study the
zero temperature instability of the normal system as the Fermi wave-vectors
mismatch of the quasi-particles (bands) is reduced and find a second order
quantum phase transition to a PDW superconducting state. From the nature of the
quantum critical fluctuations close to the superconducting quantum critical
point (SQCP), we obtain its dynamic critical exponent. It turns out to be $z=2$
and this allows to fully characterize the SQCP for dimensions $d \ge 2$.
