Structure of neutron-scattering peaks in both $s_{++}$-wave and $s_{\pm }$-wave states of an iron pnictide superconductor

We study the neutron-scattering spectrum in iron pnictides based on the random-phase approximation in the five-orbital model for fully gapped $s$-wave states with sign reversal $\left(s_{\pm }\right)$ and without sign reversal $\left(s_{++}\right)$. In the $s_{++}$-wave state, we find that a prominent hump structure appears just above the spectral gap by taking account of the quasiparticle damping $\gamma$ due to strong electron-electron correlation: as the superconductivity develops, the reduction in $\gamma$ gives rise to the large overshoot in the spectrum above the gap. The obtained hump structure looks similar to the resonance peak in the $s_{\pm }$-wave state, although the height and weight of the peak in the latter state is much larger. In the present study, experimentally observed broad spectral peak in iron pnictides is naturally reproduced by assuming the $s_{++}$-wave state.

Figure 1

(Color online) (a) FSs in iron pnictides. (b) $\omega$ dependence of $\text{Im}{\chi }^s\left(\omega ,\mathit{Q}\right)$ for the $s_{++}$-wave state $\left(\Delta =0.4\right)$ and the normal state at $T=0.01$. The “exact result” is obtained by Eq. (2) using ${256}^2$ $\mathit{k}$-meshes and 1000 $x$ meshes. The “approximate result” is obtained by Eq. (6) using ${1024}^2$ $\mathit{k}$ meshes. We put $a\left(ϵ\right)=0.05$ for $\left|ϵ\right|<3\Delta$.

Figure 2

(Color online) Obtained $\text{Im}{\chi }^s\left(\omega ,\mathit{Q}\right)$ in the $s_{++}$-wave (solid line) and normal (broken line) states for ${\gamma }_0<0.1$, using ${1024}^2$ $\mathit{k}$ meshes. We put $a\left(ϵ\right)=0.003/{\gamma }_0$ for $\left|ϵ\right|<3\Delta$.

Figure 3

(Color online) $\text{Im}{\chi }^s\left(\omega ,\mathit{Q}\right)$ for $s_{++}$-wave (solid line) and normal (broken line) states for ${\gamma }_0=0.1$, with ${\Delta }_{\text{max}}=0.07$ and ${\Delta }_{\text{min}}=0.035$. We put $a\left(ϵ\right)=0.03$ for $\left|ϵ\right|<3{\Delta }_{\text{min}}$, and $a\left(ϵ\right)=1$ for $\left|ϵ\right|>4{\Delta }_{\text{min}}$.

Figure 4

(Color online) $\text{Im}{\chi }^s\left(\omega ,\mathit{Q}\right)$ for $s_{\pm }$-wave (solid line) and normal (broken line) states, with $U=1.2$ and 1.0. We put ${\gamma }_0=0.1$ and $a\left(ϵ\right)=0.03$ for $\left|ϵ\right|<3\Delta$.