Structural and electronic properties of lead chalcogenides from first principles

We present ab initio calculations on the structural and electronic properties of the narrow-gap lead chalcogenides $\mathrm{Pb}X$ ($X=\mathrm{S}$, Se, and Te). Particular emphasis is put on the correct description of their exceptional electronic properties compared to III-V and II-VI semiconductors, such as the very small magnitude of the band gap, the unusual order of the band gaps within the series $[{E}_{g}(\mathrm{Pb}\mathrm{S})>{E}_{g}(\mathrm{Pb}\mathrm{Te})>{E}_{g}(\mathrm{Pb}\mathrm{Se})]$, and the high effective charge-carrier masses. Within standard density-functional theory (DFT), the local-density approximation (LDA) as well as the generalized gradient approximation (GGA) to the exchange-correlation potential clearly fail to describe important aspects of the band structure of these materials. This problem is overcome by applying methods that go beyond the local or semilocal approximation. We show that hybrid functionals are very successful in giving the correct results for the electronic but also for the structural properties. The lattice constants and bulk moduli as well as the fundamental band gaps and effective masses are in much better agreement with experiment than within DFT-LDA/GGA. The order of the band gaps is also properly obtained. For comparison, partially self-consistent $G{W}_{0}$ calculations are reported, yielding highly accurate values for the band gaps.