# Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

@article{Guinea2019ContinuumMF, title={Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters}, author={Francisco Guinea and Niels R. Walet}, journal={Physical Review B}, year={2019} }

We analyze a description of twisted graphene bilayers, that incorporates deformation of the layers due to the nature modern interlayer potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We shall show that flat bands result in all cases, but that their nature can be rather different. We will show how to construct a more general reduction to a continuum model, and show that even though such a model can be…

## Figures and Tables from this paper

## 74 Citations

Exact continuum model for low-energy electronic states of twisted bilayer graphene

- PhysicsPhysical Review Research
- 2019

We introduce a physically motivated minimal model for the electronic structure of twisted bilayer graphene (tBLG), which incorporates the crucial role of lattice relaxation. Our model, based on $k…

Flat bands, strains, and charge distribution in twisted bilayer
h−BN

- Physics
- 2020

We study the effect of twisting on bilayer graphene. The effect of lattice relaxation is included; we look at the electronic structure, piezo-electric charges and spontaneous polarisation. We show…

Lattice Deformation, Low Energy Models and Flat Bands in Twisted Graphene Bilayers.

- Physics
- 2019

Twisted graphene bilayers show a complex electronic structure, further modified by interaction effects. The main features can be obtained from effective models, which make use a few phenomenological…

Constrained random phase approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene

- Physics
- 2020

Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the…

Twisted Trilayer Graphene: A Precisely Tunable Platform for Correlated Electrons.

- PhysicsPhysical review letters
- 2020

It is demonstrated that the tTLG system exhibits a wide range of magic angles at which VHS merge and that the density of states has a sharp peak at the charge-neutrality point through two distinct mechanisms: the incommensurate perturbation of twisted bilayer graphene's flatbands or the equal hybridization between two bilayer moiré superlattices.

Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides

- PhysicsPhysical Review B
- 2021

Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the…

Obstruction and Interference in Low-Energy Models for Twisted Bilayer Graphene.

- PhysicsPhysical review letters
- 2020

This work finds that a careful analysis of the electron density produced by backscattering of Bloch waves from an impurity potential localized on the moiré superlattice scale can be used to tightly constrain the analytic form of the appropriate low-energy theory.

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

- Physics2D Materials
- 2019

We generalize the continuum model for Moiré structures made from twisted graphene layers, in order to include lattice relaxation and the formation of channels at very small (marginal) twist angles.…

Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene

- Physics
- 2020

Starting from a continuum-model description, we develop a microscopic weak-coupling theory for superconductivity in twisted double-bilayer graphene. We study both electron-phonon and entirely…

Interlayer coupling and strain localization in small-twist-angle graphene flakes

- PhysicsExtreme Mechanics Letters
- 2022

## References

SHOWING 1-10 OF 100 REFERENCES

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers

- PhysicsProceedings of the National Academy of Sciences
- 2018

It is shown that the modulation of the charge density significantly modifies the electronic structure, which can make an important contribution to superconductivity through electron-assisted hopping.

Structure of twisted and buckled bilayer graphene

- Physics
- 2016

We study the atomic structure of twisted bilayer graphene, with very small mismatch angles ( θ ∼ 0.28 0 ), a topic of intense recent interest. We use simulations, in which we combine a recently…

The electronic properties of bilayer graphene.

- PhysicsReports on progress in physics. Physical Society
- 2013

The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and the also discusses orbital magnetism, phonons and the influence of strain on electronic properties.

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer.

- PhysicsNature communications
- 2013

The results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.

Single-electron gap in the spectrum of twisted bilayer graphene

- Physics
- 2017

We investigate the gap in the single-electron spectrum of twisted bilayer graphene. In a perfect infinite lattice of a twisted bilayer, the gap varies exponentially in response to weak changes of the…

Non-Abelian gauge potentials in graphene bilayers.

- PhysicsPhysical review letters
- 2012

Graphene bilayers' single-particle physics is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers, which gives rise to a potential that spatially confines states at zero energy in particular regions of the moiré patterns.

All Magic Angles in Twisted Bilayer Graphene are Topological.

- PhysicsPhysical 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.

Strain solitons and topological defects in bilayer graphene

- PhysicsProceedings of the National Academy of Sciences
- 2013

Bilayer graphene has been a subject of intense study in recent years. The interlayer registry between the layers can have dramatic effects on the electronic properties: for example, in the presence…

Structural and electronic transformation in low-angle twisted bilayer graphene

- Physics
- 2017

Experiments on bilayer graphene unveiled a fascinating realization of stacking disorder where triangular domains with well-defined Bernal stacking are delimited by a hexagonal network of strain…

Lattice relaxation and energy band modulation in twisted bilayer graphene

- Physics, Materials Science
- 2017

We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice…