  We study the low energy and low momentum behavior of current correlators in a
class of holographic zero-temperature finite density critical theories which do
not respect the hyperscaling relation. The dual holographic description is
assumed to be given by probe D-branes embedded in background geometries
characterized by a dynamical critical exponent $z$ and a hyperscaling violation
exponent $\theta$. We show that a subset of these theories with $1\leq
z<2(1-\theta/d)$ exhibit a stable linearly-dispersing mode in their low energy
spectrum of excitations. This mode, which appears as a pole in the retarded
correlators of charge density and longitudinal currents, has some
characteristics similar to that of the zero sound in Fermi liquids. Given some
reasonable assumptions, we argue that the class of theories with $\theta =d-1$
that logarithmically violate the area law in the entanglement entropy in a
manner reminiscent of theories with Fermi surfaces, does \emph {not} exhibit a
zero sound-like mode in the low energy spectrum of the probe sector.
Furthermore, utilizing the holographic Wilsonian approach, we explicitly show
that such a mode has a natural interpretation as a Goldston boson arising from
the spontaneous breaking of a specific symmetry.
