Raman scattering as a probe of nematic correlations

We use the symmetry-constrained low-energy effective Hamiltonian of iron-based superconductors to study the Raman scattering in the normal state of underdoped iron-based superconductors. The incoming and scattered Raman photons couple directly to orbital fluctuations and indirectly to the spin fluctuations. We computed both couplings within the same low-energy model. The symmetry-constrained Hamiltonian yields the coupling between the orbital and spin fluctuations of only the same symmetry type. Attraction in the $B_{2g}$ symmetry channel was assumed for the system to develop the subleading instability towards the discrete in-plane rotational symmetry breaking, referred to as Ising nematic transition. We find that upon approaching this instability, the Raman spectral function develops a quasielastic peak as a function of energy transferred by photons to the crystal. We attribute this low-energy $B_{2g}$ scattering to the critical slowdown associated with the buildup of nematic correlations.

Figure 1

(a) The unit cell of a quasi-two-dimensional FeSC contains two iron atoms and two pnictogen atoms such as As (or a chalcogen atom such as Se). The atoms above and below the iron layer are denoted by crosses and by circles, respectively. The basis vectors of the iron-only lattice are denoted by $\widehat{X}$ and $\widehat{Y}$. The vectors $\widehat{x}$ and $\widehat{y}$ are chosen as the basis vectors of the two-iron-atom unit-cell lattice. (b) The two-iron-atom Brillouin zone. The $\mathrm{\Gamma }$ point hosts two hole pockets, and the $M$ point hosts two electron pockets. The solid black and dashed blue lines denote the $d_{Xz}$ and $d_{Yz}$ orbital contents, respectively. The admixture of the $d_{XY}$ orbital at the outer parts of the crossed Fermi pockets at $M$ is neglected. The polarization vectors ${\mathit{e}}^I$ and ${\mathit{e}}^S$ for the $B_{2g}$ Raman configuration are shown.

Figure 2

Feynman graphs illustrating results (18) and (19). The pair of thick blue wavy lines at the left and right ends of both graphs represents incoming and scattered photons. The black triangles represent the Aslamazov-Larkin triangular vertex giving rise to the coupling constant ${\lambda }_{AL}$ of light to the spin-nematic order parameter, ${\left({\mathbf{\Delta }}^X\right)}^2-{\left({\mathbf{\Delta }}^Y\right)}^2$, computed in the Appendix. The double wavy red lines denote the spin susceptibilities $\chi (\mathit{q},\mathrm{\Omega })$. While the graph in (a) is not specific to the $XY$ geometry, the attraction in the nematic channel $g>0$ makes it necessary to include the ladder diagrams shown in (b), giving rise to the quasielastic peak in $B_{2g}$ geometry.

Figure 3

The modeling of the quasielastic peak in the Raman response function in accordance with Eq. (32), where ${\kappa }^{\prime \prime }$ is plotted in units of $3{\lambda }_{AL}^2\gamma$ for the following choice of fitting parameters from the bottom curve to the top one: $\tau =2$ (red dashed line), $\tau =1.5$ (black thin solid line), and $\tau =1.25$ (blue thick solid line); $\overline{g}=0.2, \overline{\gamma }=5, L=10$. The peak grows when the structural transition is approached upon cooling.