Self-energy driven resonance-like inelastic neutron spectrum in $s_{++}$-wave state in Fe-based superconductors

To elucidate the pairing states in Fe-based superconductors, we perform careful calculation of the dynamical spin susceptibility $\chi^S(q, \omega)$ at very low temperatures ($T \sim 1$ meV). The feedback effect on both the self-energy and $\chi^S(q, \omega)$ from the superconducting gap are self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the $s_{+-}$-wave state, which has sign-reversal in the gap function, $\chi^S(q, \omega)$ at the nesting momentum $q = Q$ shows a resonance peak even when the system is away from the magnetic quantum-critical-point (QCP). In the $s_{++}$-wave state that has no sign-reversal, $\chi^S(q, \omega)$ shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of self-energy driven resonance-like peak in $s_{++}$-wave state proposed in our previous semi-microscopic study: The enhancement in $\chi^S(q, \omega)$ due to self-energy effect exceeds the suppression due to coherence factor effect near magnetic QCP. We stress that the hump structure in the $s_{++}$-wave state given by the FLEX method smoothly changes to resonance-like sharp peak structure as the system approaches magnetic QCP, which was not reported in our previous studies. The obtained $\omega$- and $T$-dependences of $\chi^S(q, \omega)$ in the $s_{++}$-wave state resemble to the resonance-like feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe