Intrinsic orbital moment and prediction of a large orbital Hall effect in two-dimensional transition metal dichalcogenides

Abstract

Carrying information using generation and detection of the orbital current, instead of the spin current, is an emerging field of research, where the orbital Hall effect (OHE) is an important ingredient. Here, we propose a new mechanism of the OHE that occurs in non-centrosymmetric materials. We show that the broken inversion symmetry in the 2D transition metal dichalcogenides (TMDCs) causes a robust orbital moment, which flow in different directions due to the opposite Berry curvatures under an applied electric field, leading to a large OHE. This is in complete contrast to the inversion-symmetric systems, where the orbital moment is induced only by the external electric field. We show that the valley-orbital locking as well as the OHE both appear even in the absence of the spin-orbit coupling. The non-zero spin-orbit coupling leads to the well-known valley-spin locking and the spin Hall effect, which we find to be weak, making the TMDCs particularly suitable for direct observation of the OHE, with potential application in orbitronics.

Orbital Hall effect in crystals: inter-atomic versus intra-atomic contributions

“…3 for (a) MoS 2 , as well as for (b) SnTe and PbTe. In MoS 2 , since each valley is associated with an OAM of opposite sign, one should expect that the valley Hall effect is accompanied by an OHE, as pointed out recently [36][37][38][39]. In fact, in agreement with these studies, we obtain a finite value of the intraatomic OHE in the gap for MoS 2 (black line), whereas the inter-atomic OHE vanishes (red line).…”

Orbital gyrotropic magnetoelectric effect and its strain engineering in monolayer NbX2

“…(13), viz., α 1 , α 2 and δ, are non-zero in presence of strain, and the leading terms in these three parameters are linear in strain, viz., α 1 = β 1 S, α 2 = β 2 S, and δ = γS. (14) Thus, in summary, the two parameters t and ∆ describe the electronic structure of the unstrained system, while in presence of strain we need the additional parameters β 1 , β 2 , κ, and γ, thereby resulting in six independent parameters in the model to describe the effect of the uniaxial strain. All these six parameters are tabulated in the main paper for monolayer NbX 2 , the subject of the present work.…”

“…However, the orbital degrees of freedom in TMDCs are often overlooked. Recently, we have pointed out the crucial role of the valley-orbital locking in generating a large orbital Hall current [3,14]. The valley-orbital locking, where the two different valleys K and K have opposite orbital moments, is more fundamental than the valley-spin coupling, in the sense that no SOC is necessary for the former.…”

Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching

“…The OHE has distinctive features compared to the SHE; first, the OHE originates from momentum-space orbital textures, so it universally occurs in multi-orbital systems regardless of the magnitude of SOC 12 . For example, it has been reported non-trivial orbital current can be generated in 3d transition metals, graphene, or two-dimensional transition metal dichalcogenides [13][14][15][16][17][18] . Second, theoretical calculations show that orbital Hall conductivity is much larger than spin Hall conductivity in many materials, including those commonly used for SOT such as Ta and W 10,11,13 .…”