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We elucidate the effects of defect disorder and $e$-$e$ interaction on thespectral density of the defect states emerging in the Mott-Hubbard gap of dopedtransition-metal oxides, such as Y$_{1-x}$Ca$_{x}$VO$_{3}$. A soft gap ofkinetic origin develops in the defect band and survives defect disorder for$e$-$e$ interaction strengths comparable to the defect potential and hoppingintegral values above a doping dependent threshold, otherwise only a pseudogappersists. These two regimes naturally emerge in the statistical distribution ofgaps among different defect realizations, which turns out to be of Weibulltype. Its shape parameter $k$ determines the exponent of the power-lawdependence of the density of states at the chemical potential ($k-1$) and hencedistinguishes between the soft gap ($k\geq2$) 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 isconfined by the closest defect potential and the overall spin-orbitalstructure. Such a generic behavior leads to complex non-hydrogen-like defectstates that tend to preserve the underlying $C$-type spin and $G$-type orbitalorder and can be detected and analyzed via scanning tunneling microscopy.

Defects, disorder and strong electron correlations in orbital degenerate, doped Mott insulators