High order momentum topological insulator in 2D semi-Dirac materials

TL;DR

This paper investigates the topological properties of 2D semi-Dirac materials, revealing high order momentum topological insulator behavior, anisotropic edge states, and their robustness against disorder, with implications for transport properties.

Contribution

It introduces the concept of high order momentum topological insulators in 2D semi-Dirac materials and analyzes their edge states and disorder robustness.

Findings

Edge states are anisotropic and protected by the Zak phase.

Topological protection is limited to specific momentum values.

Disorder affects edge state robustness and transport properties.

Abstract

Semi-Dirac materials in 2D present an anisotropic dispersion relation, linear along one direction and quadratic along the perpendicular one. This study explores the topological properties and the influence of disorder in a 2D semi-Dirac Hamiltonian. Anisotropic edge states appear only in one direction. Their topological protection can be rigorously founded on the Zak phase of the one-dimensional reduction of the semi-Dirac Hamiltonian, parametrically depending on one of the momenta. In general, only a single value of the momentum is topologically protected so these systems can be considered as high order momentum topological insulators. We explore the dependence on the disorder of the edge states and the robustness of the topological protection in these materials. We also explore the consequences of the high order topological protection in momentum space for the transport properties in a two-terminal configuration.