Origin of magic angles in twisted bilayer graphene: The magic ring

TL;DR

This paper explains the physical origin of magic angles in twisted bilayer graphene by linking them to the Fermi ring and charge accumulation in the AA region, enabling prediction of flat bands crucial for superconductivity.

Contribution

It identifies the role of the Fermi ring and charge distribution in AA regions as key to predicting magic angles, advancing understanding of flat band formation in TBG.

Findings

Magic angles are predicted by moire periodicity related to the Fermi ring size.

Resonant scattering on the Fermi ring leads to flat bands near the Fermi level.

Charge accumulation in AA regions influences the emergence of flat bands.

Abstract

The unexpected discovery of superconductivity and strong electron correlation in twisted bilayer graphene (TBG), a system containing only sp electrons, is considered as one of the most intriguing developments in two-dimensional materials in recent years. The key feature is the emergent flat energy bands near the Fermi level, a favorable condition for novel many-body phases, at the so-called "magic angles". The physical origin of these interesting flat bands has been elusive to date, hindering the construction of an effective theory for the unconventional electron correlation. In this work, we have identified the importance of charge accumulation in the AA region of the moire supercell and the most critical role of the Fermi ring in AA-stacked bilayer graphene. We show that the magic angles can be predicted by the moire periodicity determined by the size of this Fermi ring. The resonant criterion in momentum space makes it possible to coherently combine states on the Fermi ring through scattering by the moire potential, leading to flat bands near the Fermi level. We thus establish the physical origin of the magic angles in TBG and identify the characteristics of one-particle states associated with the flat bands for further many-body investigations.