Orbital Edelstein effect of electronic itinerant orbital motion at edges

In the study of orbital angular momentum (OAM), the focus has been\npredominantly on the intra-atomic contribution. However, recent research has\nbegun to shift towards exploring the inter-atomic contribution to OAM dynamics.\nIn this paper, we investigate the orbital Edelstein effect (OEE) arising from\nthe inter-atomic OAM at the edges. We explore the OAM texture within edge\nstates and unveil the OAM accumulation at the edges using several lattice\nmodels based on the $s$ orbital. By comparing slabs with differently shaped\nedges, we not only clarify the role of electron wiggling motion in shaping OAM\ntexture but also highlight the absence of bulk-boundary correspondence in the\naccumulation process. The topological insulator and higher-order topological\ninsulator models further confirm these findings and provide evidence for the\nrelationship between the higher-order topology and the OEE. Our study advances\nthe comprehension of orbital physics and extends its scope to higher-order\ntopological insulators.\n