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

TL;DR

This paper investigates how Dirac electrons behave on three-dimensional graphitic zeolites, revealing that their mass gap scales inversely with the surface period and is influenced by the topology of the surface.

Contribution

It introduces a model for Dirac electrons on 3D periodic curved graphene surfaces and shows how topology and spatial period affect their electronic properties.

Findings

Dirac electrons become massive near charge neutrality on these surfaces.

The band gap scales as 1/L within each mod-3 class.

Wave functions are localized around topological defects due to non-trivial Bloch phases.

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 $K'$ points of the original graphene.