Topological Aspect of Graphene Patchwork with Regular Arrays of Nano Holes

Abstract

Triangular and honeycomb lattices are dual to each other -- if we puncture holes into a featureless plane in a regular triangular alignment, the remaining body looks like a honeycomb lattice, and vice versa, if the holes are in a regular honeycomb alignment, the remaining body has a feature of triangular lattice. In this work, we reveal that the electronic states in graphene sheets with nano-sized holes in triangular and honeycomb alignments are also dual to each other in a topological sense. Namely, a regular hole array perforated in graphene can open a band gap in the energy-momentum dispersion of relativistic electrons in the pristine graphene, and the insulating states induced by triangular and honeycomb hole arrays are distinct in topology. In a graphene patchwork with regions of these two hole arrays put side by side counterpropagating topological currents emerge at the domain wall. This observation indicates that the cerebrated atomically thin sheet is where topological physics and nanotechnology meet.

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Cited by in corpus (9)

• Topological junction states and their crystalline network in chiral-symmetric systems: application to graphene nanoribbons
• $\pi$-fluxes, semi-metals and flat bands in artificial materials
• Optically controllable coupling between edge and topological interface modes of graphene metasurfaces
• Floquet Graphene Antidot Lattices
• Topological electronic states in holey graphyne
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Possible gapless helical edge states in hydrogenated graphene
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Topological property of graphene with triangular array of nanoholes