# Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect

@article{Hejazi2020HybridWC,
title={Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect},
author={Kasra Hejazi and Xiao Chen and Leon Balents},
journal={arXiv: Mesoscale and Nanoscale Physics},
year={2020}
}
• Published 30 June 2020
• Physics
• arXiv: Mesoscale and Nanoscale Physics
We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions, that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moire cell using the Hartree-Fock method. We discuss at…
16 Citations

## Figures from this paper

Orbital Chern insulator domain walls and chiral modes in twisted bilayer graphene
• Materials Science
• 2020
We consider magic-angle twisted bilayer graphene (TBG) at filling $\nu=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a
TBG IV: Exact Insulator Ground States and Phase Diagram of Twisted Bilayer Graphene
• Physics
• 2020
We derive the exact analytic insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the
TBG VI: An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Physics
• 2020
Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4) (U(4)$\times$U(4))
TBG II: Stable Symmetry Anomaly in Twisted Bilayer Graphene
• Physics
• 2020
We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with a lattice model.
Current-Driven Magnetization Reversal in Orbital Chern Insulators.
• Medicine, Physics
Physical review letters
• 2021
This work proposes a current-driven mechanism whereby reversal occurs along lines in the (current I, magnetic-field B) control parameter space with slope dI/dB=(e/h)MA_{M}(1-γ^{2})/γ, where M is the magnetization.
Domain wall competition in the Chern insulating regime of twisted bilayer graphene
• Physics, Materials Science
Physical Review B
• 2021
We consider magic-angle twisted bilayer graphene (TBG) at filling $\nu=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a
Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene
• Physics
• 2021
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly
Global phase diagram of twisted bilayer graphene above $T_c$
• Physics
• 2021
We investigate the full doping and strain-dependent phase diagram (absent superconductivity) of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that
Higher-Order Topological Superconductivity in Twisted Bilayer Graphene
We show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. C2zT -protected corner states of Majorana
Lattice model for the Coulomb interacting chiral limit of magic-angle twisted bilayer graphene: Symmetries, obstructions, and excitations
• Physics
Physical Review B
• 2021
We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized – yet

## References

SHOWING 1-10 OF 26 REFERENCES
Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality
• Physics
Physical Review Research
• 2021
We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moire flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use
Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene
• Physics
• 2021
Based on an all-band moir\'e Hartree-Fock variational method, the authors study theoretically the correlated and topological states in magic-angle twisted bilayer graphene. They construct phase
Ferromagnetism in Narrow Bands of Moiré Superlattices.
• Physics, Medicine
Physical review letters
• 2020
An intuitive picture based on extended Wannier orbitals is given, and the role of the quantum geometry of the band is emphasized, whose microscopic details may enhance or weaken ferromagnetism in moiré materials.
Independent superconductors and correlated insulators in twisted bilayer graphene
• Materials Science, Physics
Nature Physics
• 2020
When two sheets of graphene are stacked on top of each other with a small twist of angle θ  ≈ 1.1° between them, theory predicts the formation of a flat electronic band 1 , 2 . Experiments have shown
Intrinsic quantized anomalous Hall effect in a moiré heterostructure
The observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride is reported, driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1.
Nature of the Correlated Insulator States in Twisted Bilayer Graphene.
• Medicine, Materials Science
Physical review letters
• 2020
It is found that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected C_{2}T symmetry.
Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic-angle twisted bilayer graphene
• Physics
• 2020
We use the density matrix renormalization group (DMRG) to study the correlated electron states favored by the Coulomb interaction projected onto the narrow bands of twisted bilayer graphene within a
All Magic Angles in Twisted Bilayer Graphene are Topological.
• Physics, Medicine
Physical review letters
• 2019
This work proves, using an approximate low-energy particle-hole symmetry, that the gapped set of bands that exist around all magic angles have a nontrivial topology stabilized by a magnetic symmetry, provided band gaps appear at fillings of ±4 electrons per moiré unit cell.
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
Evidence is presented that near three-quarters of the filling of the conduction miniband, these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state, and measurements suggest that the system may be an incipient Chern insulator.
Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle
• Physics
Physical Review X
• 2019
We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real