# Dirac and Weyl Fermions in 3D Hopf-linked Honeycomb Lattices: Hopfene

## TL;DR

This paper introduces Hopfene, a novel 3D carbon allotrope with topologically nontrivial Hopf-link structures, which preserves graphene's Dirac points and hosts various Dirac and Weyl fermions in its electronic structure.

## Contribution

It proposes Hopfene as a new topologically nontrivial carbon allotrope with 3D Hopf-link arrays, extending graphene's electronic properties into three dimensions.

## Key findings

- Dirac points of graphene are topologically protected in Hopfene.
- Low-energy excitations include 1D, 2D, and 3D Dirac and Weyl fermions.
- Hopfene exhibits unique topological electronic properties.

## Abstract

Carbon allotropes such as diamond, nano-tube, Fullerene, and Graphene, have unique lattice symmetries of crystal lattice, but these are topologically trivial. We have proposed a topologically-nontrivial allotrope, named Hopfene, which has three-dimensional (3D) arrays of Hopf-links to bind 2D Graphene sheets both vertically and horizontally. Here, we describe the electronic structures of Hopfene by simple tight-binding calculations. We confirmed the original Dirac points of 2D Graphene were topologically protected upon the introduction of the Hopf links, and low-energy excitations are described by 1D, 2D, and 3D Dirac and Weyl Fermions.