Collective $d$-wave exciton modes in the calculated Raman spectrum of Fe-based superconductors

Calculations of the pairing interaction in multiband models of the Fe superconductors show that it is attractive in both the $A_{1g}$ ($s$-wave) and $B_{1g}$ ($d$-wave) channels. This raises the possibility that these materials may have collective excitonic modes. Here, assuming an $s$-wave ground state, we investigate the $d$-wave collective excitonic mode and its coupling to the Raman scattering.

Figure 1

(a) The Fermi surfaces in the 1 Fe/cell Brillouin zone. Here we have combined the ${\alpha }_1$ and ${\alpha }_2$ hole Fermi surfaces into one $\alpha$ sheet. For the simple example that we will consider the pairing interaction for the $A_{1g}$ ($s$-wave) ground state is described by a strength $V$ for scattering pairs between the $\alpha$ and ${\beta }_1$ and ${\beta }_2$ Fermi surfaces. The $d$-wave part of the interaction $U$ scatters $d$-wave pairs between ${\beta }_1$ and ${\beta }_2$. (b) Diagrams for the $A_{1g}$ pairing instability.

Figure 2

(a) Diagrams for the $d$-wave collective mode. Here the thick single arrow line represents the single-particle Green’s function $G\left(\mathbf{p},i{\omega }_n\right)$ and the double arrow line the Gor’kov anomalous Green’s function $F\left(\mathbf{p},i{\omega }_n\right)$ in the $A_{1g}$ state. (b) The lowest-order $U$ contribution to the Raman scattering from interband pair interactions, scattering pairs between ${\beta }_1$ and ${\beta }_2$. Here ${\gamma }_{{\beta }_i}$ is the Raman vertex on the ${\beta }_i$ Fermi surface denoted by the solid circles.

Figure 3

(Color online) Plots of the Raman response for different gap anisotropies $r$ in the absence of collective mode effects (black) and with collective contribution included (red or dark gray) for ${\lambda }_s=1$ and ${\lambda }_d=0.5$. Here the parameter $a$ has been set to 1 and a small damping term has been added. Note the changes in scale of the $r=0$ plot.

Figure 4

(Color online) Same as Fig. 3 but for ${\lambda }_s=1$ and ${\lambda }_d=0.8$.