Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene

TL;DR

This paper discovers a new 'Dirac magic' phenomenon in twisted AA-stacked multilayer graphene, characterized by multiple anisotropic Dirac cones and Lifshitz transitions, which can be tuned by twist angle and electric field.

Contribution

It introduces the concept of Dirac magic angles in twisted AA-stacked multilayer graphene and analyzes their geometric and topological origins.

Findings

Multiple anisotropic Dirac cones coexist at certain angles.

Lifshitz transitions occur due to saddle points in the band structure.

The phenomena are tunable by twist angle and electric field.

Abstract

We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moir\'e reciprocal lattice. The anisotropy of the Dirac cones and a concomitant cascade of saddle points induce a series of topological Lifshitz transitions that can be tuned by the twist angle and perpendicular electric field. We discuss the possibility of direct observation of Dirac magic as well as its consequences for the correlated states of electrons in this moir\'e system.