As a technologically important class of materials, group-IIIA oxides $M_2{\mathrm{O}}_3$ ($M$ = Al, Ga, In) have been extensively applied in various areas, yet their polaronic nature of self-trapped excess charge remains controversial. Here, utilizing the recently developed first-principles theory of polarons, we investigate the formation of hole polarons in $M_2{\mathrm{O}}_3$ to clarify whether they are small or large. We consider the most common rhombohedral and monoclinic phases of $M_2{\mathrm{O}}_3$ and reveal that an excess hole forms a highly anisotropic large polaron in rhombohedral ${\mathrm{Al}}_2{\mathrm{O}}_3$, while it also forms a large polaron in monoclinic ${\mathrm{Al}}_2{\mathrm{O}}_3$ but with much weaker anisotropy. For ${\mathrm{Ga}}_2{\mathrm{O}}_3$, our calculations confirm the formation of a small polaron in monoclinic phase, but a large polaron is more favorable in rhombohedral phase. In rhombohedral ${\mathrm{In}}_2{\mathrm{O}}_3$, the hole is found to exhibit as a large polaron with an ellipsoid feature. The drastically different polaronic characteristics in $M_2{\mathrm{O}}_3$ are explained in terms of the distinct electronic band structures and phonon spectra. This work not only clarifies the existing controversies between the available theoretical calculations and experimental observations, but it also sheds light on the potential applications of oxide materials with diverse functionalities.

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• Electron-phonon coupling
• Electronic structure
• Polarons
• Wide band gap systems
• Density functional calculations