Relaxation effects on Hartree-Fock ground states in twisted bilayer graphene at even integer fillings
Abstract
A standard approach for studying magic angle twisted bilayer graphene (MATBG)'s correlated electronic phase diagram is to project the Coulomb interaction down to effective models only involving electrons in single-particle flat bands and some nearby remote bands. We provide a novel systematic derivation of a single-particle continuum model of MATBG's single-particle properties which incorporates structural relaxation while remaining in the Lagrangian frame. We project the Coulomb interactions down to electrons occupying the flat bands of this model and compute the Hartree-Fock many-body ground states at fillings ν= ± 2. We find that incorporating relaxation effects drives the model into a semi-metallic phase at $- 2$ because of particle-hole asymmetry in the relaxed model's single-particle dispersion and because the flat band wavefunctions become more concentrated leading to an enhanced Hartree potential. Our results corroborate recent ab initio density functional theory studies which also found semi-metallic phases at −2. We discuss potential explanations for why such phases have not been seen in experiments.
Related
BibTeX
@misc{kong2026relaxation,
title = {{Relaxation effects on Hartree-Fock ground states in twisted bilayer graphene at even integer fillings}},
author = {Tianyu Kong and Alexander B. Watson and Lin Lin and Mitchell Luskin and Kevin D. Stubbs},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02815},
eprint = {2609.02815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02815},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relaxation effects on Hartree-Fock ground states in twisted bilayer graphene at even integer fillings
AU - Tianyu Kong
AU - Alexander B. Watson
AU - Lin Lin
AU - Mitchell Luskin
AU - Kevin D. Stubbs
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02815
UR - https://arxiv.org/abs/2609.02815
AB - A standard approach for studying magic angle twisted bilayer graphene (MATBG)'s correlated electronic phase diagram is to project the Coulomb interaction down to effective models only involving electrons in single-particle flat bands and some nearby remote bands. We provide a novel systematic derivation of a single-particle continuum model of MATBG's single-particle properties which incorporates structural relaxation while remaining in the Lagrangian frame. We project the Coulomb interactions down to electrons occupying the flat bands of this model and compute the Hartree-Fock many-body ground states at fillings ν= ± 2. We find that incorporating relaxation effects drives the model into a semi-metallic phase at $- 2$ because of particle-hole asymmetry in the relaxed model's single-particle dispersion and because the flat band wavefunctions become more concentrated leading to an enhanced Hartree potential. Our results corroborate recent ab initio density functional theory studies which also found semi-metallic phases at −2. We discuss potential explanations for why such phases have not been seen in experiments.
ER -