Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene

TL;DR

This paper explores flat bands and magnetic phases in magic-angle twisted monolayer-trilayer graphene, revealing how electron interactions and electric fields influence magnetic orderings.

Contribution

It introduces the study of flat bands in twisted monolayer on trilayer graphene and analyzes electron interactions and magnetic phases in this new system.

Findings

Flat bands occur near 1.16° twist angle in monolayer-trilayer graphene.

AtABC system exhibits a band gap between flat and remote bands.

Electric fields enhance magnetic ordering susceptibility.

Abstract

Starting with twisted bilayer graphene, graphene-based moir\'e materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken-symmetry phases, we further investigate the ostensibly similar magic angle AtABC system. We study the effect of electron-electron interactions in AtABC using both Hartree theory and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle, and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.