The correlated insulators of magic angle twisted bilayer graphene at zero and one quantum of magnetic flux: a tight-binding study

TL;DR

This study uses a tight-binding model to analyze correlated insulator states in magic angle twisted bilayer graphene under magnetic fields, revealing various topological and magnetic phases with potential for phase transitions.

Contribution

It provides the first atomistic tight-binding analysis of MATBG's correlated insulators under magnetic flux, highlighting mechanisms behind different ordered states.

Findings

KIVC order is the ground state at zero field for certain dopings.

Predicted insulators with Chern numbers -2, +2, and 0 under magnetic flux.

Electron-hole asymmetry influences phase stability and topological properties.

Abstract

Magic angle twisted bilayer graphene (MATBG) has become one of the prominent topics in Condensed Matter during the last few years, however, fully atomistic studies of the interacting physics are missing. In this work, we study the correlated insulator states of MATBG in the setting of a tight-binding model, under a perpendicular magnetic field of $0$ and $26.5$ T, corresponding to zero and one quantum of magnetic flux per unit cell. At zero field and for dopings of two holes ($\nu=-2$) or two electrons ($\nu=+2$) per unit cell, the Kramers intervalley coherent (KIVC) order is the ground state at the Hartree-Fock level, although it is stabilized by a different mechanism to that in continuum model. At charge neutrality, the spin polarized state is competitive with the KIVC due to the on-site Hubbard energy. We obtain a strongly electron-hole asymmetric phase diagram with robust insulators for electron filling and metals for negative filling. In the presence of magnetic flux, we predict an insulator with Chern number $-2$ for $\nu=-2$, a spin polarized state at charge neutrality and competing insulators with Chern numbers $+2$ and $0$ at $\nu=+2$. The stability of the $\nu=+2$ insulators is determined by the screening environment, allowing for the possibility of observing a topological phase transition.