Two-dimensional excitons from twisted light and the fate of the photon's orbital angular momentum

As the bound state of two oppositely charged particles, excitons emerge from optically excited semiconductors as the electronic analogue of a hydrogen atom. In the two-dimensional (2D) case, realized either in quantum well systems or truly 2D materials such as transition metal dichalcogenides, the relative motion of an exciton is described by two quantum numbers: the principal quantum number $n$, and a quantum number $j$ for the angular momentum along the perpendicular axis. Conservation of angular momentum demands that only the $j=0$ states of the excitons are optically active in a system illuminated by plane waves. Here we consider the case for spatially structured light sources, specifically for twisted light beams with non-zero orbital angular momentum per photon. Under the so-called dipole approximation where the spatial variations of the light source occur on length scales much larger than the size of the semiconductor's unit cell, we show that the photon (linear and/or angular) momentum is coupled to the center-of-mass (linear and/or angular) momentum of the exciton. Our study establishes that the selection rule for the internal states of the exciton, and thus the exciton spectrum, is independent from the spatial structure of the light source.