Supermoir\'e low-energy effective theory of twisted trilayer graphene

TL;DR

This paper develops a low-energy effective theory for twisted trilayer graphene, capturing the complex moiré-of-moiré patterns and their impact on electronic spectrum, revealing protected spectral features due to symmetries.

Contribution

It introduces a novel effective model for twisted trilayer graphene that accounts for moiré-of-moiré structures and their influence on low-energy electronic properties.

Findings

The model includes one Dirac cone and two gapped points per valley.

The spectrum exhibits a non-abelian gauge potential ensuring gauge invariance.

Numerical solutions show a fully connected spectrum protected by symmetries.

Abstract

Stacking three monolayers of graphene with a twist generally produces two moir\'e patterns. A moir\'e of moir\'e structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moir\'e lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\bf \Gamma}_M$ point of the moir\'e Brillouin zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The velocities and small gaps exhibit a spatial dependence in the moir\'e-of-moir\'e unit cell, entailing a non-abelian connection potential which ensures gauge invariance. The resulting model is numerically solved and a fully connected spectrum is obtained, which is protected by the combination of time-reversal and twofold-rotation symmetries.