Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors

We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $\varphi$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $\varphi$ 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 near an Ising-nematic transition. In both cases, the order-parameter is not a conserved quantity and the $d-$wave fermionic polarization $\mathrm{\Pi }(q,\mathrm{\Omega })$ remains finite even at $q=0$. The polarization $\mathrm{\Pi }(0,\mathrm{\Omega })$ has similar behavior in the two cases, but the relations between $\mathrm{\Pi }(0,\mathrm{\Omega })$ and the bosonic susceptibility $\chi (0, \Omega)$aredifferent,leadingtodifferentformsof$\chi^{\prime \prime} (0, \Omega)$, as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors FeSe${}_{1-x}$S${}_x$, NaFe${}_{1-x}$Co${}_x$As and BaFe${}_2$As${}_2$. We argue that the data for FeSe${}_{1-x}$S${}_x$ are well described within Pomeranchuk scenario, while the data for NaFe${}_{1-x}$Co${}_x$As and BaFe${}_2$As${}_2$ are better described within the “independent” scenario involving a composite spin order.