Abstract
Abstract
Carbon allotropes such as diamond, nano-tube, Fullerene, and Graphene were discovered and revolutionised material sciences. These structures 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. Regardless of these exotic molecular structures, the structures of materials are topologically trivial in a mathematical sense, that their bonds are connected without a link nor a knot. These days, the progress on the synthetic chemistry is significant to make various topologically non-trivial molecular structures. Topological molecules (0D) including Trefoil knots, a Hopf-link, a Möbius strip, and Borromean rings, were already realised. However, their potentially exotic electronic properties have not been sufficiently explored. Here, we propose a new 3D carbon allotrope, named Hopfene, which has periodic arrays of Hopf-links to knit horizontal Graphene sheets into vertical ones without connecting by σ bonds. We conducted an ab inito band structure calculation using a Density-Functional-Theory (DFT) for Hopfene, and found that it is well-described by a tight-binding model. 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 gapless Fermions.
Funder
Engineering and Physical Sciences Research Council
Subject
Metals and Alloys,Polymers and Plastics,Surfaces, Coatings and Films,Biomaterials,Electronic, Optical and Magnetic Materials
Cited by
5 articles.
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