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

Recent Raman scattering experiments have revealed a quasielastic peak in FeSe1-xSx 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-alpha when temperature is decreased toward the QCP, with 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 tau(-1) of this deformation as the product of the quasielastic peak frequency Gamma and the Ising-nematic thermodynamic susceptibility chi. Over a broad temperature regime, we find that tau(-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 omega(1/3), consistently with earlier theoretical predictions.