Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides.

Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTIs), protected by C_{3} rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H TMDs and reveal that 1T TMDs are identified by a Z_{4} topological invariant. As a result, when cut along appropriate directions, they host conducting edge states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for orbitronics and spin orbitronics.

Disentangling Orbital and Valley Hall Effects in Bilayers of Transition Metal Dichalcogenides.

It has been recently shown that monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase exhibit relatively large orbital Hall conductivity plateaus within their energy band gaps, where their spin Hall conductivities vanish [Canonico et al., Phys. Rev. B 101, 161409 (2020)PRBMDO2469-995010.1103/PhysRevB.101.161409; Bhowal and Satpathy, Phys. Rev. B 102, 035409 (2020)PRBMDO2469-995010.1103/PhysRevB.102.035409]. However, since the valley Hall effect (VHE) in these systems also generates a transverse flow of orbital angular momentum, it becomes experimentally challenging to distinguish between the two effects in these materials. The VHE requires inversion symmetry breaking to occur, which takes place in the TMD monolayers but not in the bilayers. We show that a bilayer of 2H-MoS_{2} is an orbital Hall insulator that exhibits a sizeable orbital Hall effect in the absence of both spin and valley Hall effects. This phase can be characterized by an orbital Chern number that assumes the value C_{L}=2 for the 2H-MoS_{2} bilayer and C_{L}=1 for the monolayer, confirming the topological nature of these orbital-Hall insulator systems. Our results are based on density functional theory and low-energy effective model calculations and strongly suggest that bilayers of TMDs are highly suitable platforms for direct observation of the orbital Hall insulating phase in two-dimensional materials. Implications of our findings for attempts to observe the VHE in TMD bilayers are also discussed.

Spin and Charge Transport of Multiorbital Quantum Spin Hall Insulators.

The fabrication of bismuthene on top of SiC paved the way for substrate engineering of room temperature quantum spin Hall insulators made of group V atoms. We perform large-scale quantum transport calculations in these two-dimensional (2D) materials to analyze the rich phenomenology that arises from the interplay between topology, disorder, valley, and spin degrees of freedom. For this purpose, we consider a minimal multiorbital real-space tight-binding Hamiltonian and use a Chebyshev polynomial expansion technique. We discuss how the quantum spin Hall states are affected by disorder, sublattice resolved potential, and Rashba spin-orbit coupling. It is also shown that these materials can be driven to a topological Anderson insulator phase by sufficiently strong disorder.