Optical selection rule of monolayer transition metal dichalcogenide by an optical vortex

We have derived the optical selection rule of monolayer transition metal dichalcogenide (TMD) for various optical vortices. Monolayer TMD, which is two-dimensional direct semiconductor, has a twofold valley degree of freedom. The valley degree of freedom can be controlled by circular polarized light. However, it is not clear how the orbital angular momentum of light relates to the valley degree of freedom. Here we clarified that the orbital angular momentum of light modifies the optical selection rule at valley points and the selection rule reflects the three-fold rotation symmetry of monolayer TMD. We expect that this modified selection rule broadens the research field of two-dimensional layered materials and spin-valleytronics. (paper)