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Titled: ORBITALHALLEFFECTAND HIGHER-ORDER TOPOLOGY IN 2D MATERIALS Abstract: A renewed interest in orbital magnetism and other orbital effects in solids raises expectations that orbital angular degrees of freedom may be eventually employed to process information in logic and memory devices. This next-generation technology has been coined as orbitronics and utilizes the orbital current as an information carrier.The orbital Hall effect (OHE) refers to the creation of a transverse flow of orbital angular momentum that is induced by a longitudinally applied electric field. I will discuss various aspects of the OHE in 2D materials. In particular, I will show that monolayers of transition metal dichalcogenides (TMDs) semiconductors in the noncentrosymmetric 2H and centrosymmetric 1T phases can be classified as higher-order topological insulators (HOTI) and exhibit OHE in their insulating phase. The higher-order topology guarantees that when cut along appropriate directions, the TMDs host conducting edge-states, which cross their bulk gaps and can transport orbital angular momentum. Our results offer the possibility of using TMDs for orbital current injection and orbital torque transfer that can surpass their spin equivalents.