A self-consistent Hartree theory for lattice-relaxed magic-angle twisted bilayer graphene

TL;DR

This paper develops a self-consistent Hartree continuum theory for twisted bilayer graphene near the magic angle, incorporating lattice relaxation effects, revealing a Lifshitz transition and a pinned ultraflat band relevant for experimental observations.

Contribution

It introduces a novel continuum model that combines lattice relaxation and Hartree interactions, explaining the emergence of a pinned ultraflat band in magic-angle twisted bilayer graphene.

Findings

Identification of a Lifshitz transition in the Fermi surface topology.

Prediction of a pinned ultraflat band at the Fermi energy.

Analytical and numerical characterization of the narrow magic angle range.

Abstract

For twisted bilayer graphene close to magic angle, we show that the effects of lattice relaxation and the Hartree interaction both become simultaneously important. Including both effects in a continuum theory reveals a Lifshitz transition to a Fermi surface topology that supports both a ``heavy fermion" pocket and an ultraflat band ($\approx 8~{\rm meV}$) that is pinned to the Fermi energy for a large range of fillings. We provide analytical and numerical results to understand the narrow ``magic angle range" that supports this pinned ultraflat band and make predictions for its experimental observation. We believe that the bands presented here are accurate at high temperature and provide a good starting point to understand the myriad of complex behaviour observed in this system.