The First Magic Angle Beyond the Chiral Limit in Twisted Bilayer Graphene
Abstract
We develop a squared-Hamiltonian description of twisted bilayer graphene beyond the chiral limit to explain why the first magic angle remains robust under lattice relaxation, while higher-order magic angles are strongly destabilized. Starting from the non-chiral Bistritzer--MacDonald model with finite same-sublattice tunneling, we show that lattice relaxation reshapes the effective confinement landscape rather than acting as a simple perturbation of the chiral theory. A central result is that the realistic relaxation-renormalized tunneling ratio lies close to a special confinement point where the oscillatory part of the symmetric confinement potential nearly cancels. This places realistic twisted bilayer graphene near a nearly uniform confinement regime. At the same time, finite same-sublattice tunneling activates an additional inter-sublattice current-like channel that competes with the chiral orbital channel. The first magic angle survives because these confinement and current-like contributions remain balanced, whereas higher-order magic angles lose this balance through stronger remote-band hybridization and enhanced real-space localization around AA regions. Our results provide a single-particle mechanism for the breakdown of the chiral magic-angle hierarchy and clarify why the experimentally relevant first magic angle remains the most stable remnant of the chiral flat-band structure.
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BibTeX
@misc{navarrolabastida2026first,
title = {{The First Magic Angle Beyond the Chiral Limit in Twisted Bilayer Graphene}},
author = {Leonardo A. Navarro-Labastida and Pierre A. Pantaleon and Francisco Guinea and Gerardo G. Naumis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08347},
eprint = {2609.08347},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08347},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The First Magic Angle Beyond the Chiral Limit in Twisted Bilayer Graphene
AU - Leonardo A. Navarro-Labastida
AU - Pierre A. Pantaleon
AU - Francisco Guinea
AU - Gerardo G. Naumis
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.08347
UR - https://arxiv.org/abs/2609.08347
AB - We develop a squared-Hamiltonian description of twisted bilayer graphene beyond the chiral limit to explain why the first magic angle remains robust under lattice relaxation, while higher-order magic angles are strongly destabilized. Starting from the non-chiral Bistritzer--MacDonald model with finite same-sublattice tunneling, we show that lattice relaxation reshapes the effective confinement landscape rather than acting as a simple perturbation of the chiral theory. A central result is that the realistic relaxation-renormalized tunneling ratio lies close to a special confinement point where the oscillatory part of the symmetric confinement potential nearly cancels. This places realistic twisted bilayer graphene near a nearly uniform confinement regime. At the same time, finite same-sublattice tunneling activates an additional inter-sublattice current-like channel that competes with the chiral orbital channel. The first magic angle survives because these confinement and current-like contributions remain balanced, whereas higher-order magic angles lose this balance through stronger remote-band hybridization and enhanced real-space localization around AA regions. Our results provide a single-particle mechanism for the breakdown of the chiral magic-angle hierarchy and clarify why the experimentally relevant first magic angle remains the most stable remnant of the chiral flat-band structure.
ER -