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

TL;DR

This paper theoretically analyzes the low-frequency Raman response near an Ising-nematic quantum critical point using a memory matrix approach, explaining experimental observations of a quasi-elastic peak and its temperature dependence.

Contribution

It introduces a memory matrix framework to connect the Raman quasi-elastic peak with nematic fluctuations and impurity scattering effects near the QCP.

Findings

The quasi-elastic peak frequency scales with inverse susceptibility and decay rate.

Critical fluctuations significantly influence the temperature dependence of the peak.

Raman response at high frequencies follows a  power law, aligning with previous predictions.

Abstract

Recent Raman scattering experiments have revealed a "quasi-elastic peak" in $\mathrm{FeSe_{1-x}S_x}$ 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}.