  Orbitronics has recently emerged as a very active research topic after
several proposals aiming to exploit the orbital degree of freedom for
charge-free electronics. In this communication, we investigate orbital
transport in selected two-dimensional systems to better understand which
parameters govern the intra-atomic and inter-atomic contributions to the
orbital Hall effect. We study the impact of the gap, the role of the materials'
topology and the influence of the disorder on spin and orbital Hall transport.
Starting from the Kane-Mele model, we describe how the orbital moment behaves
depending on the material's topology and clarify the influence of the gap on
the orbital Hall conductivity. We then extend the study to realistic
topologically trivial and non-trivial materials, and find that the topology has
little qualitative influence on the orbital Hall conductivity. In contrast, we
observe that the energy dispersion has a more dramatic impact, especially in
the presence of disorder. Remarkably, our results suggest that the intra-atomic
orbital Hall current is more robust against scattering than the inter-atomic
one, without further impact of the topological properties of the system under
consideration.
