Topological Aspect of Graphene Patchwork with Regular Arrays of Nano Holes

TL;DR

This paper explores the topological differences in electronic states of graphene sheets perforated with nano-sized holes arranged in triangular and honeycomb patterns, revealing duality and topologically distinct insulating states.

Contribution

It uncovers the topological duality of electronic states in graphene with different nano-hole arrangements and demonstrates topological currents at domain walls between these regions.

Findings

Nano-hole arrays open band gaps in graphene.

Triangular and honeycomb hole patterns induce topologically distinct insulating states.

Counterpropagating topological currents occur at domain walls.

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.