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}
}
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… Expand

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References

SHOWING 1-10 OF 26 REFERENCES
Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality
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 useExpand
Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene
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 phaseExpand
Ferromagnetism in Narrow Bands of Moiré Superlattices.
TLDR
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. Expand
Independent superconductors and correlated insulators in twisted bilayer graphene
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 shownExpand
Nature of the Correlated Insulator States in Twisted Bilayer Graphene.
TLDR
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. Expand
Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic-angle twisted bilayer graphene
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 aExpand
All Magic Angles in Twisted Bilayer Graphene are Topological.
TLDR
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. Expand
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
TLDR
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. Expand
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
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 realExpand
Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene.
We study ferromagnetism and its stability in twisted bilayer graphene. We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where theExpand
...
1
2
3
...