Electronic Raman scattering from orbital nematic fluctuations

We compute Raman scattering intensities via the lowest-order coupling to the bosonic propagator associated with orbital nematic fluctuations in a minimal model for iron pnictides. The model consists of two bands on a square lattice exhibiting four Fermi pockets and a transition from a normal to a nematic state. It is shown that the orbital fluctuations produce in the $B_{1g}$ channel strong quasielastic light scattering around the nematic critical temperature $T_n$, both above and below $T_n$. This holds for the $A_{1g}$ symmetry only below $T_n$, whereas no low-energy scattering from orbital fluctuations is found in the $B_{2g}$ symmetry. Due to the nematic distortion, the electron pocket at the $X$ point may disappear at low temperatures. Such a Lifshitz transition causes in the $B_{2g}$ spectrum a large upward shift of spectral weight in the high-energy region, whereas no effect is seen in the other symmetries.

Figure 1

Dispersion of the two bands along symmetry directions in the normal (upper panel) and nematic (middle panel) states. The Fermi energy corresponds to zero. The bottom panel shows the nematic order parameter $n_{-}$ as a function of temperature $T$. Left and right insets depict the Fermi lines in the nematic state at low temperatures and in the normal state, respectively.

Figure 2

Diagrams for the Raman susceptibility ${\chi }^{\gamma }$ and the propagator $D^{33}$ for orbital fluctuations. $\widehat{\gamma }$ denotes Raman vertices and $\widehat{{\tau }_3}$ a vertex coming from the interaction $H_1$.

Figure 3

Panels (a) and (c): Im${\chi }^{B_{1g}}\left(\omega \right)$ for temperatures below and above $T_n$, respectively. Panels (b) and (d): $S^{B_{1g}}\left(\omega \right)$ for the same temperatures.

Figure 4

Panels (a) and (c): Im${\chi }^{A_{1g}}\left(\omega \right)$ for temperatures below and above $T_n$, respectively. Panels (b) and (d): $S^{A_{1g}}\left(\omega \right)$ for the same temperatures.

Figure 5

Panels (a) and (c): Im${\chi }^{B_{2g}}\left(\omega \right)$ for temperatures below and above $T_n$, respectively. Panels (b) and (d): $S^{B_{2g}}\left(\omega \right)$ for the same temperatures.

Figure 6

(a) Black, red, and dashed lines denote the intraband, interband, and total contribution to $\mathrm{Im}{\Pi }^{33}\left(\omega \right)$, respectively. (b) Im${\Pi }^{33}\left(\omega \right)$ for several temperatures.

Figure 7

Comparison of the $A_{1g}$ spectra with (solid line) and without (dashed line) Coulomb screening. The dashed line is identical with the curve for $T=0.11$ in Fig. 4.