Self-energy driven resonancelike inelastic neutron spectrum in the s++ -wave state in Fe-based superconductors

To elucidate the pairing states in Fe-based superconductors, we perform a careful calculation of the dynamical spin susceptibility ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ at very low temperatures ($T\ensuremath{\gtrsim}1\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$). The feedback effect on both the self-energy and ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ from the superconducting gap is self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave state, which has sign reversal in the gap function, ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ at the nesting momentum $\mathbit{q}=\mathbit{Q}$ 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, ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of a self-energy driven resonancelike peak in the ${s}₊₊$-wave state proposed in our previous semimicroscopic study: The enhancement in ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ due to the self-energy effect exceeds the suppression due to the coherence factor effect near the magnetic QCP. We stress that the hump structure in the ${s}₊₊$-wave state given by the FLEX method smoothly changes to a resonancelike sharp peak structure as the system approaches the magnetic QCP, which was not reported in our previous studies. The obtained $\ensuremath{\omega}$ and $T$ dependence of ${\ensuremath{\chi}}^S(\mathbit{q},\ensuremath{\omega})$ in the ${s}₊₊$-wave states resembles the resonancelike feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.