Magnetism and hidden quantum geometry in charge neutral twisted trilayer graphene

TL;DR

This paper develops a theoretical model for mirror-symmetric magic angle twisted trilayer graphene, revealing flat bands, magnetic phase transitions, and hidden quantum geometric properties influenced by electron interactions and symmetry breaking.

Contribution

It introduces a Hubbard model for twisted trilayer graphene, analyzes magnetic and topological phases, and uncovers hidden quantum geometry in the system's flat bands.

Findings

Flat bands and Dirac cone observed in bandstructure.

Charge neutrality leads to a metallic to antiferromagnetic transition.

Hidden quantum geometry with non-trivial Berry curvature distribution.

Abstract

Here we present a theory of mirror-symmetric magic angle twisted trilayer graphene. The electronic properties are described by a Hubbard model with long range tunneling matrix elements. The electronic properties are obtained by solving the mean field Hubbard model. We obtain the bandstructure with characteristic flat bands and a Dirac cone. At charge neutrality, turning on electron-electron interactions results in metallic to antiferomagnetic phase transition, for Hubbard interaction strength considerably smaller than in other graphene multilayers. We analyze the stability of the antiferromagnetic state against the symmetry breaking induced by hexagonal boron nitride encapsulation, and mirror symmetry breaking caused by the application of electric fields that mix the Dirac cone with the flat bands. Additionally, we explore the topological properties of the system, revealing a hidden quantum geometry. Despite the flat bands having zero Chern numbers, the multiband Berry curvature distribution over the moir\'e Brillouin zone exhibits a non-trivial structure. Finally, we propose a mechanism to tune this quantum geometry, providing a pathway to control the system's topological properties.