Polarons in semilocal density functional theory: localization, many-body self-interaction, and formation energy

We develop a semilocal functional for overcoming the self-interaction of electron and hole polarons by enforcing the piece-wise linearity upon electron occupation. We obtain localized polarons with structural and electronic properties in agreement with references from a hybrid functional satisfying the same constraint. We then develop a scheme accounting for the effects of Fock exchange, further improving the formation energies. We demonstrate that the difference between the one-body and the many-body self-interaction is related to screening effects. Case studies include the electron polaron in BiVO₄, the hole polaron in MgO, and the hole trapped at the Al impurity in α-SiO₂.