# Twisted bilayer graphene with Kekule distortion: isolated flat band

## TL;DR

This paper investigates twisted bilayer graphene with Kekulé distortion induced by substrates, demonstrating that an isolated flat band with ultra-narrow bandwidth can emerge, using both Dirac Fermion and tight binding models.

## Contribution

It introduces a new approach to induce flat bands in twisted bilayer graphene via substrate-induced Kekulé distortion, combining two modeling methods for validation.

## Key findings

- Isolated flat band with ultra-narrow bandwidth can be achieved.
- Both Dirac Fermion and tight binding models yield consistent results.
- Substrate-induced Kekulé distortion effectively modifies electronic properties.

## Abstract

Twisted bilayer graphenes with magical angle exhibit strongly correlated electronic properties because of the isolated flat band at the Fermi level. We studied the twisted bilayer graphene with substrates on both layers. The substrate induce Kekul$\acute{e}$ distortion for each graphene layer. The systems are investigated by both continuous Dirac Fermion model and tight binding model. The two investigations give similar conclusion that isolated flat band with ultra-narrow bandwidth could appear.