# 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

#### 15 Citations

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… Expand

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… Expand

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))… Expand

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.… Expand

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. Expand

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… Expand

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… Expand

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… Expand

Higher-Order Topological Superconductivity in Twisted Bilayer Graphene

- Physics
- 2021

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… Expand

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… Expand

#### 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… Expand

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… Expand

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. Expand

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… Expand

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. Expand

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… Expand

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. Expand

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene

- Physics, Medicine
- Science
- 2019

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

- 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… Expand

Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene.

- Physics, Materials Science
- 2019

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 the… Expand