Breathing-Controlled Pure Orbital and Nonlinear Hall Effects in 2D Organic Kagome Frameworks

Crystalline porous organic frameworks, including covalent organic frameworks (COFs) and hydrogen-bonded organic frameworks (HOFs), provide geometrically tunable platforms for exotic electronic phenomena. Through symmetry analysis and first-principles calculations, we demonstrate that two-dimensional organic breathing kagome (BK) COF and HOF exhibit pronounced orbital Hall effect (OHE), nonlinear Hall effect (NHE), and nonequilibrium orbital magnetization (NEOM) driven by breathing-induced inversion-symmetry breaking (ISB). Due to the negligible spin-orbit coupling (SOC) in organic materials, these responses originate purely from geometric modulation, enabling reversible control of the orbital angular momentum and Berry curvature and thus switchable OHE, NHE, and NEOM. Notably, OHE persists across gaps induced by both Haldane and ISB effects, while NHE and NEOM are exclusively observed in the ISB regime and maintain breathing-tunable characteristics. Our findings identify organic BK lattices as an ideal SOC-free geometry-controllable platform for realizing and manipulating OHE and NHE.