Orbital topology induced orbital Hall effect in two-dimensional insulators

Studies of ground-state topology in quantum materials have led to the discovery of topological phases with novel Hall responses. Recently, the orbital Hall effect (OHE) has drawn growing attention; however, the origin of the large orbital Hall conductivity in insulators remains elusive. Here, we introduce the concept of orbital Chern insulators (OCIs), a previously unexplored topological phase in which orbital angular momentum drives nontrivial topology and hosts the OHE in insulating systems. We establish a comprehensive orbital-topology-based framework for systematically characterizing OCIs, and identify monolayer blue phosphorene, a material previously considered a trivial insulator, as the first pure OCI with robust topological boundary states. We demonstrate that OCI state in blue phosphorene is entirely orbital driven, and it is fully disentangled from the spin and valley degrees of freedom, which results in an OHE that can be experimentally distinguished from the spin and valley Hall effects in insulating materials. Our work suggests a new avenue for exploring orbital topology in materials for advancing orbitronics-based technologies.