Hole polaron-polaron interaction in transition metal oxides and its limit to p-type doping

Traditionally the origin of the poor p-type conductivity in some transition metal oxides (TMOs) was attributed to the limited hole concentration: the charge-compensating donor defects, such as oxygen vacancies and cation interstitials, can form spontaneously as the Fermi energy shifts down to near the valence band maximum. Besides the thermodynamic limit to the hole concentration, the limit to the hole mobility can be another possible reason, e.g., the hole carrier can form self-trapped polarons with very low carrier mobility. Although isolated hole polarons had been found in some TMOs, the polaron-polaron interaction is not well-studied. Here we show that in TMOs such as TiO$_2$ and V$_2$O$_5$, the hole polarons prefer to bind with each other to form bipolarons, which are more stable than free hole carriers or separated polarons. This pushes the hole states upward into the conduction band and traps the holes. The rise of the Fermi energy suppresses the spontaneous formation of the charge-compensating donor defects, so the conventional mechanism becomes ineffective. Since it can happen in the impurity-free TMO lattices, independent of any extrinsic dopant, it acts as an intrinsic and general limit to the p-type conductivity in these TMOs.