Not yet reviewed by Pith; the record is open.

Despite the recent success of identifying experimental signatures of the orbital Hall effect (OHE), the research on the microscopic mechanisms behind this unique phenomenon is still in its infancy. Here, using a gapped 2D Dirac material as a model system of the OHE, we develop a microscopic theory of orbital transport which captures extrinsic disorder effects non-perturbatively. We show that it predicts several hitherto unknown effects, including (i) a strong dependence of the orbital Hall conductivity with the strength and symmetry of the impurity scattering potential, and (ii) a smooth crossover from intrinsic to extrinsic OHE as a function of the Fermi energy and impurity density. In contrast to previous (perturbative) studies, the OHE is found to exhibit bona fide diffusive behavior in the dilute impurity limit, which we trace back to the dominance of skew scattering-type processes. More generally, we argue that the newly unveiled orbital skew scattering mechanism governs the diffusive OHEs of a large class of 2D materials even when the crystal structure is inversion-symmetric. Our work unveils the crucial nature of non-perturbative vertex corrections for a complete description of orbital transport and confirms common short-range impurities as key enablers of the OHE.