Band-gap switching and scaling of nanoperforated graphene

TL;DR

This paper systematically classifies graphene nanomesh structures with hexagonal nanoholes, revealing gap opening criteria, periodicity in electronic properties, and the coexistence of Dirac and flat bands, advancing understanding of nanoperforated graphene.

Contribution

It introduces a new classification framework for graphene nanomeshes based on three parameters, providing clear gap opening rules and insights into electronic band structures.

Findings

Gap opening follows a simple criterion w_1+w_2-R=3n+1.

Periodic nanoperforation affects gap sizes and scaling behavior.

Coexistence of Dirac and flat bands depends on atomic patterns.

Abstract

In this paper, a framework of {w_1, w_2, R} classification for constructing the graphene nanomesh (GNM) of zigzag-edged hexagonal nanohole is systematically built. The three integer indexes w_1, w_2, and R indicate the distances between two neighboring sides of nanoholes in two directions and the nanohole size respectively, which leading to a straightforward gap opening criteria, i.e., w_1+w_2-R=3n+1,n is integer, steered via DFT band structure calculations.The guiding rule indicates that the semimetallic and semiconducting variation is consistent with a peculiar sequence "010" and "100" ("0"/"1" represent gap closure/opening) with a period of 3 for odd and even w_1 respectively. The periodic nanoperforation induced gap sizes agreewith a linear fitting with a smaller sqrt(N_rem )/N_tot ratio, while deviates from that when (w_1+w_2)<R+1. Particularly, the {p, 1, p} and {1, q, q} structures demonstrate each unique scaling rule pertaining to the nanohole size only when n is set to zero. Furthermore, the coexistence of Dirac and flat bands is observed for {1, q, q} and {1, 1, m} structures, which is sensitive to the atomic patters