Intrinsic Topological Control of the Orbital Hall Effect in Buckled Dirac Materials

Abstract: We study the orbital Hall response in buckled two-dimensional Dirac materials using a unified framework that includes an antiferromagnetic exchange field, a perpendicular electric field, and intrinsic spin-orbit coupling. We show that the orbital Hall conductivity is considerably boosted around band-inversion points and shows different signatures across multiple electronic phases using a low-energy massive Dirac model in conjunction with Berry-curvature-based linear response theory. We find a series of quantum spin Hall, valley Hall, and anomalous Hall regimes by methodically adjusting external fields, and demonstrate how the evolution of the orbital response is controlled by the redistribution of Berry curvature between spin and valley sectors. We examine the impacts of finite temperature in more detail and find that although the response s size is suppressed by thermal broadening, the distinctive phase-dependent features remain robust. Our findings demonstrate that orbital Hall conductivity offers a sensitive band topology probe in Dirac systems and emphasize buckled two-dimensional materials as a flexible platform for engineering tunable orbital currents for orbitronic applications.