Chirality has wide ranging implications from biology to cosmology including an intimate but subtle connection to condensed matter physics. The study of chirality in quantum materials can be bolstered by utilizing resonant inelastic x-ray scattering (RIXS) spectroscopy. In a typical RIXS process, the energy of the incoming x-ray photon is resonantly tuned to match an element absorption edge, thus generating a large enhancement of the scattered intensity. As the incident radiation loses its energy and momentum to excitations inherent to the material, direct information on the dispersions of charge, spin, orbital, lattice, and other degrees of freedom such as angular momentum and chirality can be obtained. In this talk, I will present a recently developed microscopic theory of photon-phonon angular momentum transfer within the context of RIXS. I will present both the local plaquette and the angular momentum-dependent RIXS formalism. I will utilize the triangular lattice and a single helical strand to demonstrate that RIXS spectroscopy is capable of measuring circularly polarized phonon angular momentum in both two- and three- dimensional materials.
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