Topological characteristics and bulk-boundary correspondence in the orbital Hall effect

The orbital Hall effect (OHE) is attracting interest due to its fundamental science implications and potential applications in orbitronics and spintronics. Unlike the spin Hall effect, the connection between the OHE and band topology is not well understood. Here we present an approach for understanding the OHE based on analyzing the projected orbital angular momentum (POAM) spectrum. By considering monolayers of group IV elements, we demonstrate that the Wannier charge centers of the POAM spectrum display topologically nontrivial windings. The orbital Hall conductivity is found to form a plateau within the band gap as a direct consequence of the Chern number carried by the POAM spectrum. Importantly, we show that the topological orbital Hall phase yields a new form of bulk-boundary correspondence, which features gapless states in the POAM spectrum and induces nonzero orbital textures at the boundaries that would be amenable to experimental verification through circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES) experiments. Our study presents a systematic method for investigating the topological OHE and provides a pathway for its broader exploration in two-dimensional materials.