Spectral weight and spatially modulated instabilities in holographic superfluids

Free fermions form a Fermi surface, which results in non-zero spectral weight at low energy and finite wavevector kF. In this work, we find similar features in holographic phases dual to strongly coupled quantum superfluid matter. At zero temperature, the phases we consider exhibit semi-local criticality in the IR and all the charge is carried by the scalar condensate outside the black hole horizon. Depending on the value taken by the IR critical exponents, we find Fermi surfaces in the transverse sector, Fermi shells in the longitudinal sector or no spectral weight at all. When there is non-zero transverse spectral weight, the IR can be subject to an instability at finite wavevector, the endpoint of which is likely a spatially modulated phase.