Twisted Trilayer Graphene: a Precisely Tunable Platform for Correlated Electrons

TL;DR

This paper introduces twisted trilayer graphene with two twist angles as a tunable platform for studying correlated electron behaviors, revealing multiple magic angles where van Hove singularities enhance correlations.

Contribution

It develops a comprehensive low-energy electronic structure model for tTLG with arbitrary twist angles, uncovering the existence of multiple magic angles and the mechanisms behind van Hove singularity merging.

Findings

Identification of multiple magic angles in tTLG.

Demonstration of van Hove singularity merging mechanisms.

Development of a general electronic structure model for tTLG.

Abstract

We introduce twisted trilayer graphene (tTLG) with two independent twist angles as an ideal system for the precise tuning of the electronic interlayer coupling to maximize the effect of correlated behaviors. As established by experiment and theory in the related twisted bilayer graphene system, van Hove singularities (VHS) in the density of states can be used as a proxy of the tendency for correlated behaviors. To explore the evolution of VHS in the twist-angle phase space of tTLG, we present a general low-energy electronic structure model for any pair of twist angles. We show that the basis of the model has infinite dimensions even at a finite energy cutoff and that no Brillouin zone exists even in the continuum limit. Using this model, we demonstrate that the tTLG system exhibits a wide range of magic angles at which VHS merge and the density of states has a sharp peak at the charge-neutrality point through two distinct mechanisms: the incommensurate perturbation of twisted bilayer graphene's flat bands or the equal hybridization between two bilayer moir\'e superlattices.