Orbital Edelstein effect of electronic itinerant orbital motion at edges

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