Bi, Cr and Ag dopants in PbTe and SnTe: Impact of the host band symmetry on doping properties by ab initio calculations

Doping properties of Bi, Cr and Ag dopants in thermoelectric and topological materials PbTe and SnTe are analyzed based on density functional theory calculations in the local density approximations and the large supercell method. In agreement with experiment, in both PbTe and SnTe, Bi is a donor and Ag is an acceptor with a vanishing magnetic moment. In contrast, Cr is a resonant donor in PbTe, and an resonant acceptor in SnTe. We also consider the electronic structure of cation vacancies in PbTe and SnTe, since these abundant native defects induce $p$-type conductivity in both hosts. The quantitatively different impact of these dopants/defects on the host band structure of PbTe and SnTe (level energies, band splittings, band inversion, and a different level of hybridization between dopant and host states) is explained based on the group-theoretical arguments.