Normal densities in cool quantum critical superfluids

It is common belief that at zero temperature, a phase that spontaneously breaks a U(1) symmetry becomes entirely superfluid, ie the normal density vanishes. This is indeed the case in a variety of systems, such as weakly-coupled Helium, BCS superconductors and relativistic superfluids described by a quantum effective action originally written by Son. Here, I will show that this expectation fails in certain classes of holographic superfluids, such as those with a Lifshitz-invariant critical ground state with Lifshitz exponent z¿d+2 (d is the number of spatial dimensions), thus clarifying previous results in earlier literature. Time permitting, I will conclude by commenting on the relevance of these results for recent measurements in overdoped high Tc superconductors revealing an anomalously low superfluid density at odds with BCS theory expectations.