  Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at
selected atoms in materials, including particle-hole transitions between the
valence and conduction bands. These transitions are governed by fundamental
properties of the corresponding Bloch wave-functions, including orbital and
magnetic degrees of freedom, and quantum geometric properties such as the Berry
curvature. In particular, orbital angular momentum (OAM), which is closely
linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We
demonstrate how information on such OAM textures can be extracted from the
circular dichroism in RIXS. Based on accurate modeling with first-principles
treatment of the key ingredient -- the light-matter interaction -- we simulate
dichroic RIXS spectra for the prototypical transition metal dichalcogenide
MoSe$_2$ and the two-dimensional topological insulator 1T$^\prime$-MoS$_2$.
Guided by an intuitive picture for the optical selection rules, we discuss how
the momentum-dependent OAM manifests itself in the dichroic RIXS signal if one
controls the momentum transfer. Our calculations are performed for typical
experimental geometries and parameter regimes, and demonstrate the possibility
of observing the predicted circular dichroism in forthcoming experiments. Thus,
our work establishes a new avenue to observing Berry curvature and topological
states in quantum materials.
