Graphene: Free electron scattering within an inverted honeycomb lattice

TL;DR

This paper introduces a simple plane-wave model with a single fitting parameter that outperforms the standard tight-binding model in predicting the detailed electronic band structure of graphene nanostructures, aligning closely with density-functional theory results.

Contribution

It presents a novel, simple plane-wave approach for modeling graphene's electronic states, capturing features beyond the tight-binding model, including electron-hole asymmetry and nanostructure-specific bands.

Findings

Accurately reproduces detailed band structures of graphene nanostructures.

Identifies hierarchies of nonmetallic armchair nanoribbons.

Explains energy splitting in zigzag nanoribbons due to symmetry breaking.

Abstract

Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that include electron-hole asymmetry and the detailed electronic bands of basic graphene nanostructures (e.g., nanoribbons with different edge terminations) are beyond the capability of such simple model. Here we show that a similarly simple plane-wave solution for the one-electron states of an atom-based two-dimensional potential landscape, defined by a single fitting parameter (the scattering potential), performs better than the standard tight-binding model, and levels to density-functional theory in correctly reproducing the detailed band structure of a variety of graphene nanostructures. In particular, our approach identifies the three hierarchies of nonmetallic armchair nanoribbons, as well as the doubly-degenerate flat bands of free-standing zigzag nanoribbons with their energy splitting produced by symmetry breaking. The present simple plane-wave approach holds great potential for gaining insight into the electronic states and the electro-optical properties of graphene nanostructures and other two-dimensional materials with intact or gapped Dirac-like dispersions.