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.

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

References in corpus (16)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Crystalline Insulators
• Scheme to Achieve Silicon Topological Photonics
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Graphene Antidot Lattices - Designed Defects and Spin Qubits
• Electron fractionalization in two-dimensional graphenelike structures
• Wannier representation of Z_2 topological insulators
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Experimental evidence of chiral symmetry breaking in Kekulé-ordered graphene
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Tailoring Dirac fermions by in-situ tunable high-order moire pattern in graphene-monolayer xenon heterostructure
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Quantum simulation of honeycomb lattice model by high-order moiré pattern
• Possible gapless helical edge states in hydrogenated graphene