Topological carbon allotropes: paradigm shift for materials innovation

Abstract

Topology is a central concept of mathematics, which allows us to distinguish two isolated rings with linked ones. In material science, researchers discovered topologically different carbon allotropes in a form of a cage, a tube, and a sheet, which have unique translational and rotational symmetries, described by a crystallographic group theory, and the atoms are arranged at specific rigid positions in 3-dimensional ($D$) space. However, topological orders must be robust against deformations, so that we can make completely different families of topological materials. Here we propose various topological structures such as knots and links using covalent $\sigma$ bonds of carbon atoms, while allowing various topologically equivalent arrangements using weak $\pi$ bonds. By extending this idea, we invented a new 3D carbon allotrope, Hopfene, which has periodic arrays of Hopf-links to knit horizontal Graphene sheets into vertical ones without connecting by $\sigma$ bonds.

19 pages, 14 figures

References in corpus (12)

• Electric Field Effect in Atomically Thin Carbon Films
• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• The electronic properties of graphene
• The Raman Fingerprint of Graphene
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• An sp-hybridized molecular carbon allotrope, cyclo[18]carbon
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions
• Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene
• Singlet superconductivity phase in carbon nanotubes
• Lattice deformation on flat-band modulation in 3D Hopf-linked carbon allotrope: Hopfene

Cited by in corpus (2)

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