Type-III Dirac Cones from Degenerate Directionally Flat Bands: Viewpoint from Molecular-Orbital Representation

TL;DR

This paper introduces a systematic method to generate type-III Dirac cones from degenerate directionally flat bands using molecular-orbital representation, applicable to various two- and four-band models without fine-tuning.

Contribution

The authors develop a novel approach employing molecular-orbital representation to create type-III Dirac cones from flat bands, expanding the design principles for topological materials.

Findings

Method successfully produces type-III Dirac cones in multiple models

No fine-tuning of hopping parameters needed

Demonstrated applicability to two- and four-band systems

Abstract

We present a systematic method of creating type-III Dirac cones from degenerate directionally flat bands. Here, the directionally flat band means a completely dispersionless band only in a certain direction. The key strategy is to retain one of the directionally flat bands while making the other dispersive, by adding a perturbation having a selected form of a Hamiltonian matrix. Such a form of a perturbation is found by using the "molecular-orbital representation" which we have developed to describe flat-band models. The models thus obtained host type-III Dirac cones even without fine-tuning hopping parameters. To demonstrate the ubiquity of this method, we study concrete examples of two-band models and a four-band model.