Zero Sound in Strange Metallic Holography

TL;DR

This paper investigates zero sound modes in holographic models of strange metals with Lifshitz scaling, revealing conditions under which these quasi-particles exist and analyzing their properties through Green's functions and conductivity calculations.

Contribution

It provides a holographic analysis of zero sound in strange metals, identifying the critical Lifshitz exponent where zero sound exists and characterizing its dispersion and damping.

Findings

Zero sound exists for z<2 in Lifshitz holography.

Zero sound dispersion is linear in momentum with damping proportional to k^2/z.

Zero sound appears only when the spectral function is a delta function at zero frequency.

Abstract

One way to model the strange metal phase of certain materials is via a holographic description in terms of probe D-branes in a Lifshitz spacetime, characterised by a dynamical exponent z. The background geometry is dual to a strongly-interacting quantum critical theory while the probe D-branes are dual to a finite density of charge carriers that can exhibit the characteristic properties of strange metals. We compute holographically the low-frequency and low-momentum form of the charge density and current retarded Green's functions in these systems for massless charge carriers. The results reveal a quasi-particle excitation when z<2, which in analogy with Landau Fermi liquids we call zero sound. The real part of the dispersion relation depends on momentum k linearly, while the imaginary part goes as k^2/z. When z is greater than or equal to 2 the zero sound is not a well-defined quasi-particle. We also compute the frequency-dependent conductivity in arbitrary spacetime dimensions. Using that as a measure of the charge current spectral function, we find that the zero sound appears only when the spectral function consists of a single delta function at zero frequency.