Localized gap states in oxides and their anti-doping

In standard unreactive doping, adding charge carrier to a compound results in a shift of the Fermi level towards the conduction band for electron doping and towards the valence band for hole doping. We point out a curious case of anti-doping where p-type (n-type) doping results in band gap opening, moving the previously occupied (unoccupied) bands to the principal conduction (valence) band and reducing conductivity. We find that this is a generic behavior for a class of materials and find inverse-design principles for detecting such materials. For instance, early transition metal oxides where the sum of composition-weighed formal oxidation states is positive (e.g., TiO_2-x, CeO_2-x, Ba₂Ti₆O₁₃ and Ba₄Ti₁₂O₂₇) tend to form in the band gap an intermediate trapped electron band localized on reduced cation orbitals. Upon p-type doping of such materials, hole annihilates a trapped electron on just one cation; consequently, electronically equivalent cation sublattices in the undoped compound become electronically distinct after doping, i.e., symmetry breaking. We give specific theoretical predictions for target compounds where hole and electron anti-doping might be observed experimentally for the first time.