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arXiv · 1007.0590

Zero Sound in Strange Metallic Holography

Carlos Hoyos-Badajoz·Andy O'Bannon·Jackson M. S. Wu
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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.

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Carlos Hoyos-Badajoz, Andy O'Bannon, Jackson M. S. Wu. 2010-10-08. Zero Sound in Strange Metallic Holography. https://doi.org/10.1007/jhep09(2010)086

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