Fano resonances in multigap Fe based superconductors and complexity for material design

The Fano resonance in the superconducting gaps (or ``shape resonance'' or ``Feshabch resonance'' ) in multigap superconductors [A Bianconi \textit{Sol. State Commun.}89, 933 (1994)] has been proposed as the mechanism for high Tc in Fe-based superconductors and related compounds [D Innocenti et al \textit{Supercond. Sci. Technol.}, 015012 (2011)] near the Lifshitz transition for a vanishing Fermi surface in a superlattice of layers or wires, in the proximity of a lattice, electronic, magnetic instability with competing interactions that give complex systems. The multiscale phase separation from nano-scale to micron scale in K0.8Fe1.6Se2. [ A Ricciet al \textit{Phys. Rev.}B 84, 060511 (2011)] has been detected by a mixed real space and momentum space probe: scanning nano focused X-ray diffraction like in La2CuO4+y [M. Fratini, et al \textit{Nature}466, 841 (2010) and [N. Poccia et al \textit{Nature Materials}10, 733 (2011)] showing scale free structural organization of dopants favoring in the high Tc phase. The results on KFeSe show phase separation, percolating superconductivity, competing with percolating magnetism and shape resonances in the superconducting gaps.