Graphene with 3√3 × 3√3 triangular nanoholes has a topologically trivial Fermi-level gap but nontrivial obstructed atomic limit bands that produce two flat edge-localized bands in ribbons.
Periodic Behavior of Topology in Graphene with Nanohole Array
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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.
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2026 1verdicts
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Topological property of graphene with triangular array of nanoholes
Graphene with 3√3 × 3√3 triangular nanoholes has a topologically trivial Fermi-level gap but nontrivial obstructed atomic limit bands that produce two flat edge-localized bands in ribbons.