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We elucidate the effects of defect disorder and $e$-$e$ interaction on the spectral density of the defect states emerging in the Mott-Hubbard gap of doped transition-metal oxides, such as Y$_{1-x}$Ca$_{x}$VO$_{3}$. A soft gap of kinetic origin develops in the defect band and survives defect disorder for $e$-$e$ interaction strengths comparable to the defect potential and hopping integral values above a doping dependent threshold, otherwise only a pseudogap persists. These two regimes naturally emerge in the statistical distribution of gaps among different defect realizations, which turns out to be of Weibull type. Its shape parameter $k$ determines the exponent of the power-law dependence of the density of states at the chemical potential ($k-1$) and hence distinguishes between the soft gap ($kgeq2$) and the pseudogap ($k<2$) regimes. Both $k$ and the effective gap scale with the hopping integral and the $e$-$e$ interaction in a wide doping range. The motion of doped holes is confined by the closest defect potential and the overall spin-orbital structure. Such a generic behavior leads to complex non-hydrogen-like defect states that tend to preserve the underlying $C$-type spin and $G$-type orbital order and can be detected and analyzed via scanning tunneling microscopy.
The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature
We explore the competiton of doped holes and defects that leads to the loss of orbital order in vanadate perovskites. In compounds such as La$_{1-{sf x}}$Ca$_{,sf x}$VO$_3$ spin and orbital order result from super-exchange interactions described by a
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting
We study the surface of a three-dimensional spin chiral $mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that con
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emer