We analyze how the magnetic disorder affects the properties of the two-band $s_pm$ and $s_{++}$ models, which are subject of hot discussions regarding iron-based superconductors and other multiband systems like MgB$_2$. We show that there are several
cases when the transition temperature $T_c$ is not fully suppressed by magnetic impurities in contrast to the Abrikosov-Gorkov theory, but a saturation of $T_c$ takes place in the regime of strong disorder. These cases are: (1) the purely interband impurity scattering, (2) the unitary scattering limit. We show that in the former case the $s_pm$ gap is preserved, while the $s_{++}$ state transforms into the $s_pm$ state with increasing magnetic disorder. For the case (2), the gap structure remains intact.
High-$T_c$ superconductors with CuO$_2$ layers, manganites La$_{1-x}$Sr$_x$MnO$_3$, and cobaltites LaCoO$_3$ present several mysteries in their physical properties. Most of them are believed to come from the strongly-correlated nature of these materi
als. From the theoretical viewpoint, there are many hidden rocks in making the consistent description of the band structure and low-energy physics starting from the Fermi-liquid approach. Here we discuss the alternative method -- multielectron approach to the electronic structure calculations for the Mott insulators -- called LDA+GTB (local density approximation + generalized tight-binding) method. Its origin is a straightforward generalization of the Hubbard perturbation theory in the atomic limit and the multiband $p-d$ Hamiltonian with the parameters calculated within LDA. We briefly discuss the method and focus on its applications to cuprates, manganites, and cobaltites.
Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T_c cuprates phase diagram. There are at least two distinct proposals on the critical concentration an
d its physical origin. First one is associated with the pseudogap formation for p<p*, with p~0.2. Another one relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p_{opt}~0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.
