Orbital and Spin Hall effect: Effect of symmetry breaking and Density-Functional results for MoS₂

The Orbital Hall effect (OHE) is the transverse flow of orbital moment in a solid in response to an applied electric field, analogous to the flow of spin moment in the spin Hall effect (SHE). The effect is fundamentally different in solids with broken inversion symmetry, where an intrinsic orbital moment is present even without the electric field. Using a tight-binding model Hamiltonian for a simple cubic lattice with two atoms in the unit cell, we study the OHE as a function of the deviation from the inversion symmetry by computing the orbital and spin Berry curvatures. Our work shows that both OHE and SHE are much stronger in broken symmetry materials. As a concrete example, we present our results from density-functional calculations for the 2D transition-metal-dichalcogenide (TMDC) materials such as MoS₂, a broken symmetry system. Our work suggests that the TMDC's and other broken symmetry solids, because of their more robust OHE, would be good materials for the experimental observation of the OHE, which is so far not conclusively established by experiments.