Periodic Behavior of Topology in Graphene with Nanohole Array

Abstract

We derive a way to diagnose band topology for graphene with triangular and/or honeycomb array of nanoholes directly from the lattice constant of superstructure $m\sqrt{3}\times m\sqrt{3}$ with integer $m$. Taking into account the $C_{6v}$ crystalline symmetry respected by nanoholes and their array, we demonstrate that nontrivial topology appears periodically with $m$ with period two (six) for triangular (honeycomb) array. These behaviors are verified by Wyckoff positions of Wannier centers and parity index of valence bands at high-symmetry points in Brillouin zone. The results provide a convenient guide for material design of topological electronic states based on graphene derivatives.

arXiv comment10 pages, 3 figures, 2 tables + Supplementary material (3 pages, 4 tables)

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