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

TL;DR

This paper investigates the dynamical response of a near-critical nematic order parameter in Fe-based superconductors, comparing theoretical models with Raman scattering data to identify the nature of the critical fluctuations.

Contribution

It distinguishes between Pomeranchuk and independent critical degrees of freedom scenarios in explaining Raman responses in Fe-based superconductors.

Findings

FeSe$_{1-x}$S$_x$ data fit Pomeranchuk scenario

NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$ data fit independent spin order scenario

Different relations between polarization and susceptibility lead to distinct Raman signatures

Abstract

We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $\phi$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $\phi$ 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 near an Ising-nematic transition. In both cases, the order-parameter is not a conserved quantity and the $d-$wave fermionic polarization $\Pi (q, \Omega)$ remains finite even at $q=0$. The polarization $\Pi (0, \Omega)$ has similar behavior in the two cases, but the relations between $\Pi (0, \Omega)$ and the bosonic susceptibility $\chi (0, \Omega)$ are different, leading to different forms of $\chi^{\prime \prime} (0, \Omega)$, 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.