Modern Approach to Orbital Hall Effect Based on Wannier Picture of Solids

Abstract: In the field of orbital dynamics and orbital transport, a particularly important quantity is the so-called orbital Hall conductivity (OHC), which is expressed in terms of operators of velocity and orbital angular momentum (OAM). To overcome the difficulties in treating the unbounded position operator, very often atom-centered approximations are used, which capture only a part of the local contributions to the OAM operator. Here, we promote a new approach to quantify the OAM operator in the basis of Wannier functions, which is based on the modern theory of orbital magnetization and which captures both local and itinerant contributions to the OHC. By performing first-principles calculations for various materials, we show that significant corrections to the OHC by non-local effects arise when compared to common approximations. Our approach improves the understanding of the OAM in solids and allows for a precise estimation of various orbital effects in complex materials.