Projector augmented wave method with spin-orbit coupling: Applications to simple solids and zincblende-type semiconductors

Using the fully relativistic projector augmented wave (PAW) approach, we address the relevance of spin-orbit coupling for the structural properties of several solids. Results available in the literature obtained either via an all-electron full potential linearized augmented plane wave (FLAPW) method with spin-orbit treated by a second-variation procedure or via a PAW method in which spin-orbit is added to a scalar relativistic picture are used to critically estimate the soundness of our data. We construct scalar and fully relativistic PAW data sets for 26 new elements and use them to calculate the lattice constants and the bulk moduli of 56 solids finding that relativistic effects beyond the scalar relativistic ones change slightly some lattice constants and bulk moduli in the presence of fifth- or sixth-row elements, while no change above the numerical threshold is found in the other cases. Moreover, we study the spin-orbit-induced splittings of the electron energy bands of a few zincbende-type semiconductors and we show that the fully relativistic PAW method remains accurate also in the presence of light elements such as boron or nitrogen: The splittings of the ${\Gamma }_{8v}$ and ${\Gamma }_{7v}$ valence states and of the ${\Gamma }_{8c}$ and ${\Gamma }_{7c}$ conduction states agree with FLAPW within a few meV.

Figure 1

Band structure of GaAs along the $\Lambda$, $\Delta$, and $\Sigma$ lines of the Brillouin zone. The two spin-orbit-induced splittings studied in this work are indicated in the figure.

Figure 2

Differences between the PBE lattice constants calculated with the present PAW method and FLAPW (Ref. 24, continuous line). Red dots show the differences between the PAW results of Ref. 35 and FLAPW. Diamonds show the FR $-$ SR differences when they are larger than $\pm$3 mÅ. Different diamond colors correspond to different functionals as indicated in the inset.

Figure 3

Differences between the PBE bulk moduli calculated with the present PAW method and FLAPW (Ref. 24, continuous line). Red dots show the differences between the PAW results of Ref. 35 and FLAPW. Diamonds show FR $-$ SR differences when they are larger than $\pm 5$ kbar. Diamonds occurring in the same point have been split by $\pm 1$ kbar to make them visible. Different diamond colors correspond to different functionals as indicated in the inset.