Dirac electrons on three-dimensional graphitic zeolites --- a scalable mass gap

Abstract

A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the tight-binding model that the low-energy band structure around the charge neutrality point is dominated by the topology (cubic or gyroid) of the periodic surface as well as by the spatial period $L$ in modulo 3 in units of the lattice constant. In both of cubic and gyroid cases the Dirac electrons become massive around the charge neutrality point, where the band gap is shown to scale as $1/L$ within each mod-3 class. Wave functions around the gap are found to have amplitudes sharply peaked around the topological defects that are required to deform the graphene sheet into a three-dimensional periodic surface, and this is shown to originate from non-trivial Bloch phases at $K$ and $K^{\prime }$ points of the original graphene.

5 pages, 6 figures

References in corpus (4)

• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Helicoidal Graphene Nanoribbons: Chiraltronics
• Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry

Cited by in corpus (4)

• Three-dimensional porous graphene networks expand graphene-based electronic device applications
• Electric Properties of Dirac Fermions Captured into 3D Nanoporous Graphene Networks
• Dirac Fermion kinetics in three-dimensionally curved graphene
• Quantum Hall effect in three-dimensional graphene