# Flat Bands and High Chern Numbers in Twisted Multilayer Graphene

## TL;DR

This paper analyzes the electronic properties of twisted multilayer graphene, revealing that flat bands with high Chern numbers occur at specific 'magic' angles, with implications for topological phases.

## Contribution

It extends the chiral model to multilayer graphene, showing the equivalence of magic angles with bilayer cases and constructing flat band eigenfunctions with nontrivial topology.

## Key findings

- Magic angles are identical to those in twisted bilayer graphene.
- Flat bands have Chern number -n, indicating nontrivial topology.
- Band separation at Dirac points varies with tunneling strength.

## Abstract

Motivated by recent Physical Review Letters of Wang-Liu and Ledwith-Vishwanath-Khalaf, we study Tarnopolsky-Kruchkov-Vishwanath chiral model of two sheets of $n$-layer Bernal stacked graphene twisted by a small angle using the framework developed by Becker-Embree-Wittsten-Zworski. We show that magic angles of this model are exactly the same as magic angles of chiral twisted bilayer graphene with multiplicity. For small inter-layer tunneling potentials, we compute the band separation at Dirac points as we turning on the tunneling parameter. Flat band eigenfunctions are also constructed using a new theta function argument and this yields a complex line bundle with the Chern number $-n$.