# Spectral gaps in graphene antidot lattices

## TL;DR

This paper investigates how the spectral gap in graphene antidot lattices depends on various parameters, providing mathematical insights into the gap creation process in periodically perforated graphene sheets.

## Contribution

It offers new spectral analysis results on the size and dependence of energy gaps in graphene with periodic obstacles, advancing understanding of electronic properties in such nanostructures.

## Key findings

- Spectral gaps depend on lattice parameters.
- Mathematical bounds for gap sizes are established.
- Results inform design of graphene-based electronic devices.

## Abstract

We consider the gap creation problem in an antidot graphene lattice, i.e. a sheet of graphene with periodically distributed obstacles. We prove several spectral results concerning the size of the gap and its dependence on different natural parameters related to the antidot lattice.