Low frequency Raman response near Ising-nematic quantum critical point: a memory matrix approach

Abstract

Recent Raman scattering experiments have revealed a "quasi-elastic peak" in $\mathrm{FeS}{\mathrm{e}}_{1-\mathrm{x}}{\mathrm{S}}_{\mathrm{x}}$ near an Ising-nematic quantum critical point (QCP) \cite{zhang17}. Notably, the peak occurs at sub-temperature frequencies, and softens as $T^{\alpha }$ when temperature is decreased toward the QCP, with $\alpha >1$. In this work, we present a theoretical analysis of the low-frequency Raman response using a memory matrix approach. We show that such a quasi-elastic peak is associated with the relaxation of an Ising-nematic deformation of the Fermi surface. Specifically, we find that the peak frequency is proportional to ${\tau }^{-1}{\chi }^{-1}$, where $\chi$ is the Ising-nematic thermodynamic susceptibility, and ${\tau }^{-1}$ is the decay rate of the nematic deformation due to an interplay between impurity scattering and electron-electron scattering mediated by critical Ising-nematic fluctuations. We argue that the critical fluctuations play a crucial role in determining the observed temperature dependence of the frequency of the quasi-elastic peak. At frequencies larger than the temperature, we find that the Raman response is proportional to ${\omega }^{1/3}$, consistently with earlier predictions \cite{klein18a}.

arXiv comment6 pages + 5 figures

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