  Monolayer transition metal dichalcogenides host tightly-bound excitons, which
dominate their optoelectronic response even at room temperatures. Light beams
are often used to study these materials with the polarization - often termed as
the spin angular momentum of the light - providing the mechanism for exciting
excitonic states. Light beams, however, can also carry an orbital angular
momentum by creating helical structures of their phase front. In this work, we
consider a Laguerre-Gaussian beam possessing an orbital angular momentum in
addition to the spin angular momentum to create excitons in monolayer
transition metal dichalcogenides. We derive optical selection rules that govern
the allowed transitions to various exciton series using symmetry arguments. Our
symmetry considerations show that we can create dark excitons using these
high-order optical beams opening up new avenues for creating long-lived dark
excitons with the potential of exploiting them in quantum information
processing and storage.
