Theory of neutron scattering as a probe of the superconducting gap in the iron pnictides

Inelastic neutron scattering provides a probe for studying the spin and momentum structure of the superconducting gap. Here, using a two-orbital model for the Fe-pnictide superconductors and a random-phase approximation–BCS approximation for the dynamic spin susceptibility, we explore the scattering response for various gaps that have been proposed.

Figure 1

(Color online) (a) Fermi surface of the two-orbital model in the large 1-Fe/cell Brillouin zone. The ${\alpha }_{1/2}$ Fermi-surface sheets are hole pockets given by $E_{-}\left({\mathbf{k}}_F\right)=0$, and the ${\beta }_{1/2}$ sheets are electron pockets given by $E_{+}\left({\mathbf{k}}_F\right)=0$. The nesting vectors $\mathbf{q}=\left(\pi ,0\right)$ and $\mathbf{q}\ast =\left(\pi /2,0\right)$ are indicated by the dotted and dashed lines, respectively. (b) RPA spin susceptibility ${\chi }_{\text{RPA}}^{″}\left(\mathbf{q},\omega \right)$ versus frequency in the normal state $\left[\Delta \left(\mathbf{k}\right)=0\right]$ for $\mathbf{q}=\left(\pi ,0\right)$ and $\mathbf{q}\ast =\left(\pi /2,0\right)$.

Figure 2

(Color online) RPA dynamic spin susceptibility ${\chi }_{\text{RPA}}^{″}\left(\mathbf{q},\omega \right)$ versus frequency in the spin singlet superconducting state for the sign-reversed $s$-wave gap (solid line) and the extended $s$-wave gap (dashed line) for (a) $\mathbf{q}=\left(\pi ,0\right)$ and (b) $\mathbf{q}\ast =\left(\pi /2,0\right)$.

Figure 3

(Color online) RPA spin susceptibility (a) ${\chi }_{+-}^{″}\left(\mathbf{q},\omega \right)$ and (b) ${\chi }_{zz}^{″}\left(\mathbf{q},\omega \right)$ versus frequency for $\mathbf{q}=\left(\pi ,0\right)$ in the spin triplet superconducting state for a $p_x$-wave gap (solid line), a sign-reversed $p$-wave gap (dashed line), and a $p_x+i{p}_y$-wave gap (dotted line).

Figure 4

(Color online) RPA spin susceptibility (a) ${\chi }_{+-}^{″}\left(\mathbf{q},\omega \right)$ and (b) ${\chi }_{zz}^{″}\left(\mathbf{q},\omega \right)$ versus frequency for $\mathbf{q}\ast =\left(\pi /2,0\right)$ in the spin triplet superconducting state for a $p_x$-wave gap (solid line), a sign-reversed $p$-wave gap (dashed line), and a $p_x+i{p}_y$-wave gap (dotted line).