We present self-consistent calculations of the multi-gap structure measured in some Fe-based superconductors. These materials are known to have structural disorder in real space and a multi-gap structure due to the $3d$ Fe-orbitals contributing to a
complex Fermi surface topology with hole and electron pockets. Different experiments identify three s-wave like superconducting gaps with a single critical temperature ($T_c$). We investigate the temperature dependence of these gaps by a multi-band Bogoliubov-deGennes theory at different pockets in the presence of effective hybridizations between some bands and an attractive temperature dependent intra-band interaction. We show that this approach reproduces the three observed gaps and single $T_c$ in different compounds of Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$, providing some insights on the inter-band interactions.
Impurity doping like Zn atoms in cuprates were systematically studied to provide important information on the pseudogap phase because this process substantially reduces $T_c$ without effect $T^*$. Despite many important results and advances, the norm
al phase of these superconductors is still subject of a great debate. We show that the observed Zn-doped data can be reproduced by constructing a nanoscale granular superconductor whose resistivity transition is achieved by Josephson coupling, what provides also a simple interpretation to the pseudogap phase.
We develop a model for high-Tc superconductors based on an electronic phase separation where low-and high-density domains are formed. At low temperatures this system may act as a granular superconductor forming an array of Josephson junctions. Cuprat
es are also known to have low superfluid densities and strong correlation effects. Both characteristics activate a negative Josephson coupling due to frustration that leads to spontaneous currents responsible for the weak ferromagnetic order. This original approach reproduces the observed onset of spontaneous magnetic signal and its dependence on the doping level.
