Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides

TL;DR

This paper provides a comprehensive analysis of the intrinsic orbital Hall effect in monolayer transition metal dichalcogenides, exploring its origin, tunability via doping and strain, and its relation to the spin Hall effect.

Contribution

It introduces a detailed theoretical framework and models to understand and tune the orbital Hall effect in 2D TMDCs, highlighting its fundamental nature compared to the spin Hall effect.

Findings

OHE is more fundamental than SHE in TMDCs.

Hole doping and strain can tune the OHE.

Orbital moments induce spin moments via spin-orbit coupling.

Abstract

Orbital Hall effect (OHE) is the phenomenon of transverse flow of orbital moment in presence of an applied electric field. Solids with broken inversion symmetry are expected to exhibit a strong OHE due to the presence of an intrinsic orbital moment at individual momentum points in the Brillouin zone, which in presence of an applied electric field, flows in different directions causing a net orbital Hall current. Here we provide a comprehensive understanding of the effect and its tunability in the monolayer 2D transition metal dichalcogenides (TMDCs). Both metallic and insulating TMDCs are investigated from full density-functional calculations, effective $d$-band tight-binding models, as well as a minimal four-band model for the valley points that captures the key physics of the system. For the tuning of the OHE, we examine the role of hole doping as well as the change in the band parameters, which, e. g., can be controlled by strain. We demonstrate that the OHE is a more fundamental effect than the spin Hall effect (SHE), with the momentum-space orbital moments inducing a spin moment in the presence of the spin-orbit coupling, leading to the SHE. The physics of the OHE, described here, is relevant for 2D materials with broken inversion symmetry in general, even beyond the TMDCs, providing a broad platform for future research.