First-principles indicators of metallicity and cation off-centricity in the IV-VI rocksalt chalcogenides of divalent Ge, Sn, and Pb

We use first-principles density functional theory to calculate the phonon frequencies, electron localization lengths, Born effective charges, dielectric response, and conventional electronic structures of the IV-VI chalcogenide series. The goals of our work are twofold: first, to determine the detailed chemical composition of lone pairs and, second, to identify the factors that cause lone pairs to favor high- or low-symmetry environments. Our results show that the traditional picture of cation s-p mixing causing localization of the lone pair lobe is incomplete, and instead the p states on the anion also play an important role. In addition these compounds reveal a delicate balance between two competing instabilities—structural distortion and tendency to metallicity—leading, at the same time, to anomalously large Born effective charges as well as large dielectric constants. The magnitude of the LO-TO splitting, which depends on the relative strength of both instabilities, shows a trend consistent with the structural distortions in these compounds.