# SU(3) fermions in a three-band Graphene-like model

## TL;DR

This paper explores complex geometric phase structures in two-dimensional fermion models beyond the standard Dirac cone, revealing new three-band Dirac structures and Landau level quantization related to SU(3) symmetry.

## Contribution

It introduces a family of three-band models with intricate geometric phases and demonstrates their realization in a Graphene-like lattice, extending understanding beyond SU(2) Dirac physics.

## Key findings

- Identification of three-fold degeneracies with SU(3) geometric phases
- Development of a tight-binding model exhibiting three-band Dirac cones
- Discovery of non-standard Landau level quantization influenced by SU(3) phases

## Abstract

Two-dimensional Graphene is fascinating because of its unique electronic properties. From a fundamental perspective, one among them is the geometric phase structure near the Dirac points in the Brillouin zone, owing to the SU(2) nature of the Dirac cone wave functions. We ask if there are geometric phase structures in two dimensions which go beyond that of a Dirac cone. Here we write down a family of three-band continuum models of non-interacting fermions which have more intricate geometric phase structures. This is connected to the SU(3) nature of the wavefunctions near three-fold degeneracies. We also give a tight-binding free fermion model on a two-dimensional Graphene-like lattice where the three-fold degeneracies are realized at fine-tuned points. Away from them, we obtain new "three-band" Dirac cone structures with associated non-standard Landau level quantization, whose organization is strongly affected by the non-SU(2) or beyond-Dirac geometric phase structure of the fine-tuned points.