Bipolaron anisotropic flat bands, Hall mobility edge, and metal-semiconductor duality of overdoped high-$T_c$ oxides

Hole bipolaron band structure with two flat anisotropic bands is derived for oxide superconductors. Strong anisotropy leads to one-dimensional localization in a random field which explains the metal-like value of the Hall effect and the semiconductorlike doping dependence of resistivity of overdoped oxides. Doping dependence of $T_c$ and ${\lambda }_H\mathrm{}\left(0\right)\mathrm{}$ as well as the low-temperature dependence of resistivity, of the Hall effect, $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ and robust features of angle-resolved photoemission spectroscopy of several high-$T_c$ copper oxides are explained.