Effects of spin-orbit coupling on the optical response of a material

We investigate the effects of spin-orbit coupling on the optical response of materials. In particular, we study the effects of the commutator between the spin-orbit coupling part of the potential and the position operator on the optical matrix elements using density functional theory calculations within the generalized gradient approximation. By means of a formalism that separates a fully relativistic Kleinman-Bylander pseudopotential into the scalar-relativistic and spin-orbit-coupling parts, we calculate the contribution of the commutator arising from spin-orbit coupling to the squared optical matrix elements of isolated atoms, monolayer transition-metal dichalcogenides, and topological insulators. In the case of isolated atoms from H (Z=1) to Bi (Z=83), the contribution of spin-orbit coupling to the squared matrix elements can be as large as 14%. On the other hand, in the cases of monolayer transition-metal dichalcogenides and topological insulators, we find that this contribution is less than 1% and that it is sufficient to calculate the optical matrix elements and subsequent physical quantities without considering the commutator arising from spin-orbit coupling.