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.