# Topological flat bands in twisted trilayer graphene

## TL;DR

This paper investigates the band structure and topology of twisted trilayer graphene, revealing the presence of topologically nontrivial flat bands at a magic angle around 1.12°, which can be tuned by electric fields.

## Contribution

It provides a detailed continuum model analysis of the band topology and flat bands in twisted trilayer graphene, highlighting its potential for studying correlated topological physics.

## Key findings

- Magic angle for flat bands is about 1.12°
- Small twist angles induce tiny gaps at Dirac points
- Valley Chern numbers depend on twist angle and electric field

## Abstract

Twisted trilayer graphene (TLG) may be the simplest realistic system so far, which has flat bands with nontrivial topology. Here, we give a detailed calculation about its band structures and the band topology, i.e. valley Chern number of the nearly flat bands, with the continuum model. With realistic parameters, the magic angle of twisted TLG is about 1.12$^{\circ}$, at which two nearly flat bands appears. Unlike the twisted bilayer graphene, a small twist angle can induce a tiny gap at all the Dirac points, which can be enlarged further by a perpendicular electric field. The valley Chern numbers of the two nearly flat bands in the twisted TLG depends on the twist angle $\theta$ and the perpendicular electric field $E_\perp$. Considering its topological flat bands, the twisted TLG should be an ideal experimental platform to study the strongly correlated physics in topologically nontrivial flat band systems. And, due to its reduced symmetry, the correlated states in twisted TLG should be quite different from that in twisted bilayer graphene and twisted double bilayer graphene.