Orbital Hall effect and topology on a two-dimensional triangular lattice: from bulk to edge

TL;DR

This paper explores the emergence of topological phases and the orbital Hall effect in a multi-orbital model on a triangular lattice, revealing edge state behaviors and the impact of disorder in two-dimensional materials.

Contribution

It introduces a comprehensive analysis of topological phases and orbital Hall effects in a triangular lattice model, highlighting the role of symmetry-breaking and edge state properties.

Findings

Four distinct topological phases identified.

Orbital Hall effect with unique characteristics observed.

Edge states carry orbital angular momentum in insulating phase.

Abstract

We investigate a generalized multi-orbital tight-binding model on a triangular lattice, a system prevalent in a wide range of two-dimensional materials, and particularly relevant for simulating transition metal dichalcogenide monolayers. We show that the interplay between spin-orbit coupling and different symmetry-breaking mechanisms leads to the emergence of four distinct topological phases [Eck, P., \textit{et al.}, Phys. Rev. B, 107 (11), 115130 (2023)]. Remarkably, this interplay also triggers the orbital Hall effect with distinguished characteristics. Furthermore, by employing the Landauer-B\"uttiker formula, we establish that in the orbital Hall insulating phase, the orbital angular momentum is carried by edge states present in nanoribbons with specific terminations. We also show that, as expected, they do not have topological protection against the disorder of the edge states belonging to a first-order topological insulator.