Low-frequency Raman response near the Ising-nematic quantum critical point: A memory-matrix approach
Xiaoyu Wang, Erez Berg
Abstract
Recent Raman scattering experiments have revealed a quasielastic peak in ${\mathrm{FeSe}}_{1\ensuremath{-}\mathrm{x}}{\mathrm{S}}_{\mathrm{x}}$ near an Ising-nematic quantum critical point (QCP) [Zhang et al., PNAS 118, 20 (2021)]. Notably, the peak occurs at subtemperature frequencies, and softens as ${T}^{\ensuremath{\alpha}}$ when temperature is decreased toward the QCP, with $\ensuremath{\alpha}>1$. This temperature dependence is inconsistent with an impurity scattering scenario, and suggests that quantum critical fluctuations play an important role. In this work,we incorporate these effects in the framework of a memory matrix approach. The quasielastic peak is associated with the relaxation of an Ising-nematic deformation of the Fermi surface. We identify the dynamical scattering rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$ of this deformation as the product of the quasielastic peak frequency $\mathrm{\ensuremath{\Gamma}}$ and the Ising-nematic thermodynamic susceptibility $\ensuremath{\chi}$. Over a broad temperature regime, we find that ${\ensuremath{\tau}}^{\ensuremath{-}1}(T)$ exhibits a quasilinear dependence on temperature, in qualitative agreement with experiments. This behavior reflects a crossover from quantum critical scaling to a regime where the lifetime is governed by scattering from quasielastic thermal fluctuations. At frequencies larger than the temperature, we find that the Raman response is proportional to ${\ensuremath{\omega}}^{1/3}$, consistently with earlier theoretical predictions.