Dynamical susceptibility of a near-critical nonconserved order parameter and quadrupole Raman response in Fe-based superconductors

Abstract

We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $\ensuremath{\phi}$, which undergoes a continuous transition towards nematic order with a $d$-wave form factor. We consider two cases: (a) when $\ensuremath{\phi}$ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter. In both cases, the order parameter is not a conserved quantity and the $d$-wave fermionic polarization $\mathrm{\ensuremath{\Pi}}(q,\mathrm{\ensuremath{\Omega}})$ remains finite even at $q=0$. The polarization $\mathrm{\ensuremath{\Pi}}(0,\mathrm{\ensuremath{\Omega}})$ has similar behavior in the two cases, but the relations between $\mathrm{\ensuremath{\Pi}}(0,\mathrm{\ensuremath{\Omega}})$ and the bosonic susceptibility $\ensuremath{\chi}(0,\mathrm{\ensuremath{\Omega}})$ are different, leading to different forms of ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(0,\mathrm{\ensuremath{\Omega}})$, as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x},{\mathrm{NaFe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{As}$, and ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$.