Abstract. Disorder Ð impurities and defects violating the ideal long-range order Ð is always present in solids. It can result in interesting and sometimes unexpected effects in multiband superconductors, especially if the superconductivity is unconventional, thus having symmetry other than the usual s-wave. This paper uses the examples of iron-based pnictides and chalcogenides to examine how both nonmagnetic and magnetic impurities affect superconducting states with s AE and s order parameters. We show that disorder causes the transition between s AE and s states and examine what observable effects this transition can produce.

We study the spin resonance peak in recently discovered iron-based superconductors. The resonance peak observed in inelastic neutron scattering experiments agrees well with predicted results for the extended s-wave (s ± ) gap symmetry. Recent neutron scattering measurements show that there is a disparity between longitudinal and transverse components of the dynamical spin susceptibility. Such breaking of the spin-rotational invariance in the spin-liquid phase can occur due to spin-orbit coupling. We study the role of the spin-orbit interaction in the multiorbital model for Fe-pnictides and show how it affects the spin resonance feature.Keywords Fe-based superconductors · Spin-resonance peak · Spin-orbit coupling The nature of the superconductivity and gap symmetry and structure in the recently discovered Fe-based superconductors (FeBS) are the most debated topics in condensed matter community [1]. These quasi twodimensional systems shows a maximal T c of 55 K placing them right after high-T c cuprates. the Fermi surface (FS) which in the undoped systems consists of two hole and two electron sheets. Nesting between these two groups of sheets is the driving force for the spin-density wave (SDW) long-range magnetism in the undoped FeBS and the scattering with the wave vector Q connecting hole and electron pockets is the most probable candidate for superconducting pairing in the doped systems. In the spin-fluctuation studies [2,3,4], the leading instability is the extended s-wave gap which changes sign between hole and electron sheets (s ± state) [5].Neutron scattering is a powerful tool to measure dynamical spin susceptibility χ(q, ω). It carries information about the order parameter symmetry and gap structure. For the local interactions (Hubbard and Hund's exchange), χ can be obtained in the RPA from the bare electron-hole bubble χ 0 (q, ω) by summing up a series of ladder diagrams to give χ(q, ω)where U s and I are interaction and unit matrices in orbital space, and all other quantities are matrices as well. Scattering between nearly nested hole and electron Fermi surfaces in FeBS produce a peak in the normal state magnetic susceptibility at or near q = Q = (π, 0). For the uniform s-wave gap, sign∆ k = sign∆ k+Q and there is no resonance peak. For the s ± order parameter as well as for an extended non-uniform s-wave symmetry, Q connects Fermi sheets with the different signs of gaps. This fulfills the resonance condition for the interband susceptibility, and the spin resonance peak is formed at a frequency below Ω c = min (|∆ k | + |∆ k+q |)

We study the spin resonance in the superconducting state of iron-based materials within multiband models with two unequal gaps, L and S , on different Fermi-surface pockets. We show that, due to the indirect nature of the gap entering the spin susceptibility at the nesting wave vector Q, the total gap˜ in the bare susceptibility is determined by the sum of gaps on two different Fermi-surface sheets connected by Q. For the Fermi-surface geometry characteristic of most iron pnictides and chalcogenides, the indirect gap is either˜ = L + S or = 2 L . In the s ++ state, spin excitations below˜ are absent unless additional scattering mechanisms are assumed. The spin resonance appears in the s ± superconducting state at frequency ω R ˜ . Comparison with available inelastic neutron-scattering data confirms that what is seen is the true spin resonance and not a peak inherent to the s ++ state.

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Here we review experimental data on the peak in inelastic neutron scattering (INS) and superconducting gaps extracted from various experimental techniques. Comparison of energy scales gives the confidence that the observed peak in INS for most materials is the true spin resonance.