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 (≈8meV) 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.
@article{arxiv.2404.17638,
title = {A self-consistent Hartree theory for lattice-relaxed magic-angle twisted bilayer graphene},
author = {Mohammed M. Al Ezzi and Liangtao Peng and Zhengyu Liu and Jonah Huang Zi Chao and Gayani N. Pallewela and Darryl Foo and Shaffique Adam},
journal= {arXiv preprint arXiv:2404.17638},
year = {2024}
}