Orbital Hall effect in bilayer transition metal dichalcogenides

The orbital Hall effect (OHE) is analogous to the spin Hall effect (SHE) and consists in the appearance of a transverse orbital angular momentum current as a response to a longitudinally applied electric field. It has been predicted that transition metal dichalcogenides (TMDs) monolayers exhibit rather large OHE in the absence of SHE. However, valley Hall effect (VHE) also contributes to a transverse flow of orbital angular momentum current in monolayer TMDs. Therefore, it becomes experimentally difficult to discriminate between the orbital and the valley Hall effects in them.
Using Density Functional Theory, we show that the 2H-structural phase of a MoS₂ bilayer exhibits large orbital Hall signal in its insulating phase, in the absence of both SHE and VHE. This strongly indicates that bilayers of TMDs are highly suitable platforms for direct observation of the orbital Hall insulating phase in two-dimensional (2D) materials. To explore the physics behind our DFT calculations we have also built an effective low-energy relatively simple model to examine the main transport characteristics of these systems. We topologically characterize the TMD monolayers and bilayers of in terms of orbital Chern numbers and relate their values with the edge states in TMD nanoribbons.