Topological property of graphene with triangular array of nanoholes

TL;DR

This paper theoretically investigates the topological properties of graphene with a triangular array of nanoholes, revealing trivial and nontrivial band structures and localized edge states.

Contribution

It identifies the topological nature of band gaps and edge states in graphene with nanohole arrays, highlighting complex topological behaviors.

Findings

Energy gap at Γ point linked to band inversion and parity change.

Deep valence bands exhibit obstructed atomic limit (OAL) characteristics.

Localized edge states associated with nontrivial topological bands.

Abstract

The nontrivial band topology for graphene with regular arrays of nanoholes with $C_{6v}$ symmetry is investigated theoretically. For the case of $3\sqrt{3} \times 3\sqrt{3}$ triangular array of nanoholes, we find an energy gap at $\Gamma$ point around the Fermi level associated with a band inversion which induces change in parity indices, whereas deep below the Fermi level there are a bunch of valence bands characterized as obstructed atomic limit (OAL) which also accommodate imbalance in parity indices. This band structure renders the gap at the Fermi level topologically trivial and carrying no edge states, while the nontrivial band topology of the OAL manifests in two flat bands in the ribbon structure associated with localized electronic states at ribbon edges. The present results exhibit rich topological behaviors in graphene derivatives waiting for explorations.