Zero sound in strange metals with hyperscaling violation from holography

Understand

Hyperscaling violating `strange metal' phase of heavy fermion compounds can be described holographically by probe D-branes in the background of a Lifshitz space-time (dynamical exponent $z$ and spatial dimensions $d$) with hyperscaling violation (corresponding exponent $\theta$).

• Without the hyperscaling violation, strange metals are known to exhibit zero sound mode for $z<2$ analogous to the Fermi liquids.
• In this paper, we study its fate in the presence of hyperscaling violation and find that in this case the zero sound mode exists for $z < 2(1+|\theta|/d)$, where the positivity of the specific heat and the null energy condition of the background dictate that $\theta<0$ and $z\geq 1$.
• However, for $z \geq 2(1+|\theta|/d)$, there is no well-defined quasiparticle for the zero sound.