Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems

Abstract: The geometric structure of quantum states plays a fundamental role in determining the intrinsic dynamics of electrons in solids. In this work, we study the geometric origin of orbital angular momentum and its transport in a general two-band electronic system. Without assuming any symmetry or dimensional constraints, we show that the orbital Berry curvature, which governs the orbital Hall effect, can be universally expressed as the product of the band energy and the square of the Berry curvature. This highlights the central role of Berry curvature in engineering orbital Hall responses. We also discuss the applicability of our framework by analyzing a realistic model. Our findings underscore the geometric universality of itinerant intrinsic orbital dynamics.