Effect of disorder on the electronic Raman scattering in the superconducting state of iron pnictides

Electronic Raman scattering measures a polarization-dependent scattering intensity which can provide information about the location of nodes in the energy gap of an unconventional superconductor as well as its overall symmetry. In this paper, we calculate the Raman intensity in the presence of disorder for several models of the iron pnictide superconducting state. We include, for completeness, $d$-wave and isotropic $s_{\pm }$ responses in addition to more realistic extended $s_{\pm }$ superconducting gaps. The effect of disorder is modeled using a self-consistent $T$-matrix approximation, and is studied in the limits of isotropic and intraband-only scattering. We show how recent experiments on $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ may be consistent with “node lifting” by intraband disorder.

Figure 1

Diagrams representing the SCTMA. The dashed lines are scattering off an impurity and the single line is the self-consistent Green’s function.

Figure 2

(Color online) Quasiparticle density of states $N\left(\omega \right)$ for isotropic $s_{\pm }$ state, normalized to normal state density of states $N_0$ vs $\omega /{\Delta }_0$, where $\pm {\Delta }_0$ is the value of the gap on hole and electron sheets. $N_0$ is assumed constant on all Fermi sheets. Shown are various interband impurity scattering rates $\Gamma$ in units of ${\Delta }_0$.

Figure 3

(Color online) Raman response Im $\chi \left(\omega \right)$ vs $\omega /\Delta$ for both $B_{1g}$ and $B_{2g}$ polarizations for an $s_{\pm }$ state as in Fig. 2 for various interband impurity scattering rates $\Gamma$, in units of $\Delta$.

Figure 4

(Color online) Density of states $N\left(\omega \right)/{\Delta }_0$ vs energy $\omega /{\Delta }_0$ for a $d$-wave superconductor for various values of scattering rate $\Gamma /{\Delta }_0$ in unitarity limit.

Figure 5

(Color online) Effect of disorder on $T=0$ Raman response of $d$ wave state vs energy $\omega /{\Delta }_0$. Shown are two polarizations, $B_{1g}$ and $B_{2g}$, for various values of scattering rate $\Gamma /{\Delta }_0$ in unitarity limit.

Figure 6

Fermi surface from a five-orbital tight binding model with parameters chosen to match the density functional theory result (Ref. 43).

Figure 7

(Color online) Clean $B_{1g}$ and $B_{2g}$ spectra for the model of the superconducting state defined in Ref. 2 and in Eq. (7, 8, 9, 10).

Figure 8

(Color online) Density of states $N\left(\omega \right)/N_0$ for the extended $s$-wave state given in equations. Equations (7, 8, 9, 10) vs $\omega /{\Delta }_0$ for unitary intraband scattering rates $\Gamma /{\Delta }_0$. Insert shows low-energy behavior.

Figure 9

(Color online) Raman intensity for the extended $s$-wave state given in equations. Equations (7, 8, 9, 10) vs $\omega /{\Delta }_0$ for various unitary intraband scattering rates $\Gamma /{\Delta }_0$ and polarization states $B_{1g}$ and $B_{2g}$ in the 2-Fe zone. Insert: low-energy region.

Figure 10

(Color online) The density of states for an extended $s$-wave state given in equations. Equations (7, 8, 9, 10) vs $\omega /{\Delta }_0$ for unitary isotropic scattering rates $\Gamma /{\Delta }_0$.

Figure 11

(Color online) Raman intensity for an extended $s$-wave state of Fig. 10 for various unitary isotropic scattering rates $\Gamma /{\Delta }_0$ and polarization states $B_{1g}$ and $B_{2g}$ in the 2-Fe zone. Insert: low-energy region.