# Evidence for flat zero-energy bands in bilayer graphene with a periodic defect lattice

## TL;DR

This study uses ab initio calculations to show that periodic defect lattices in bilayer graphene induce flat zero-energy bands at the Fermi level, revealing potential for tailored electronic properties.

## Contribution

It demonstrates that periodic intercalation of carbon atoms creates flat bands in bilayer graphene, linking defect patterns to electronic behavior.

## Key findings

- Flat doubly degenerate bands appear at the Fermi level.
- Periodic defects induce a non-Abelian flux network.
- Electronic properties can be tailored via defect patterning.

## Abstract

In this work, we perform ab initio calculations, based on the density functional theory, of the effects on the graphene bilayer when we intercalate carbon atoms between the layers. We use the unit cell of the bilayer to construct larger unit cells (supercells), positioning a single carbon atom in the hollow position between the monolayers and periodically replicating the supercell. By increasing the size of the unit cell and consequently, the periodicity of the inserted atoms, we are able to minimize the carbon-carbon interaction and therefore infer the changes in the electronic, vibrational and thermal behavior of the bilayer when the intercalated atoms do not interact with each other. The main result, concerning the electronic properties, is the appearance of a doubly degenerate flat band at the Fermi level. These states are interpreted as coming from the periodic deformation of the bilayer due to the inserted atoms. It acts as a non-Abelian flux network creating zero energy at bands as predicted by San-Jose, Gonz\'alez and Guinea in 2012. Since the periodic strain field associated to the defect array has such a strong influence on the electronic properties of the bilayer, it may be useful for practical applications. For instance, it can act as frozen-in magnetic-like field flux tubes. All-carbon nanostructures can then be designed to have electronic behavior at different regions tailored by the chosen defect pattern.