Probing the pairing symmetry of the iron pnictides with electronic Raman scattering

An important issue in the study of the iron-arsenic-based superconductors is the symmetry of the superconducting gap, a problem complicated by multiple gaps on different Fermi-surface sheets. Electronic Raman scattering is a flexible bulk probe which allows one in principle to determine gap magnitudes and test for gap nodes in different regions of the Brillouin zone by employing different photon polarization states. Here we calculate the clean Raman intensity for $A_{1g}$, $B_{1g}$, and $B_{2g}$ polarizations and discuss the peak structures and low-energy power laws which might be expected for several popular models of the superconducting gap in these systems.

Figure 1

(Color online) Fermi surface of model Fe pnictide represented in unfolded (one-Fe) Brillouin zone. The crystalline $a,b$ axes are indicated in top right of the panel (blue) and the polarization geometries for incoming and scattering photon polarizations are denoted for $B_{1g}$ and $B_{2g}$ geometries. Note that our symmetry notation is rotated by $45°$ with respect to the lattice symmetries.

Figure 2

The anisotropic energy gaps around the four Fermi-surface sheets as a function of angle $\theta$ shown in Fig. 1. For the $\beta$ sheets, the solid line is for $r_{\beta }=1.4$ and the dotted line for $r_{\beta }=0.6$ [see Eq. (14)].

Figure 3

(Color online) Raman response of the state with energy gap Eq. (10) for $r=1.4$. Black/gray (black/red) lines denote $B_{1g}/B_{2g}$ and light gray/dark gray (green/blue) is the unscreened/screened $A_{1g}$, respectively. Note that our symmetry classifications are according to the geometry shown in Fig. 1. For lattice classifications, $B_{1g}$ and $B_{2g}$ should be interchanged.

Figure 4

(Color online) The Raman response of the state with energy gap Eq. (10) for $r=0.6$. Black/gray (black/red) lines denote $B_{1g}/B_{2g}$, respectively, light gray/dark gray (green/blue) is unscreened/screened $A_{1g}$.

Figure 5

(Color online) The screened $A_{1g}$ Raman response for two bands with ${\Delta }_{1,2}\left(\theta \right)$ proportional to $\left[1+r\text{cos}\left(4\theta \right)\right]/\left(1+r\right)$ with $r=0.2$ and the maximum gap on Fermi surface 1 equal to ${\Delta }_0$ and on Fermi surface 2 equal to ${\Delta }_0/2$. ($\text{black}=\text{screened}$ $A_{1g}$ for band 1, gray (red)$=\text{screened}$ $A_{1g}$ for band 2, light gray (green)$=\text{mixing}$ term, dark gray (blue)$=\text{total}$ response).

Figure 6

(Color online) The $B_{1g},B_{2g}$ and screened $A_{1g}$ Raman spectra for a four-sheeted Fermi surface, with $r_{\beta }=1.4$. Black line corresponds to each contribution from the ${\beta }_{1,2}$ bands, gray (red) line to the ${\alpha }_1$ band, light gray (green) line to the ${\alpha }_2$, and dark gray (blue) line is the total response. Note that for the $A_{1g}$ case (bottom panel) there is an interference term in addition to the sum of the contributions from each band. The energy gaps used are defined in the text.

Figure 7

(Color online) Same as Fig. 6 but for $r_{\beta }=0.6$.

Figure 8

(Color online) Same as Fig. 6 but for different Raman vertices, given by Eq. (15).

Figure 9

(Color online) Polarization dependence Raman response for the $s\pm$ state, having energy gaps given by Eq. (16) and Raman vertices given by Eq. (15). Color scales, denoting contributions from each band and the total response, are the same as in Figs. 6, 7, 8.