scholarly journals Real-Space Approach for the Electronic Calculation of Twisted Bilayer Graphene Using the Orthogonal Polynomial Technique

2019 ◽  
Vol 29 (4) ◽  
pp. 455 ◽  
Author(s):  
Hoang Anh Le ◽  
Van Thuong Nguyen ◽  
Van Duy Nguyen ◽  
Van-Nam Do ◽  
Si Ta Ho
Keyword(s):  
Time Evolution ◽  
Scaling Law ◽  
Bilayer Graphene ◽  
Real Space ◽  
Computational Method ◽  
Time Evolution Operator ◽  
Lattice Space ◽  
Auto Correlation Function ◽  
Technical Issues ◽  
Twisted Bilayer Graphene

We discuss technical issues involving the implementation of a computational method for the electronic structure of material systems of arbitrary atomic arrangement. The method is based on the analysis of time evolution of electron states in the real lattice space. The Chebyshev polynomials of the first kind are used to approximate the time evolution operator.  We demonstrate that the developed method is powerful and efficient since the computational scaling law is linear. We invoked the method to study the electronic properties of special twisted bilayer graphene whose atomic structure is quasi-crystalline. We show the density of states of an electron in this graphene system as well as the variation of the associated time auto-correlation function. We find the fluctuation of electron density on the lattice nodes forming a typical pattern closely related to the typical atomic pattern of the quasi-crystalline bilayer graphene configuration.

scholarly journals Magnetism of magic-angle twisted bilayer graphene

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Javad Vahedi ◽  
Robert Peters ◽  
Ahmed Missaoui ◽  
Andreas Honecker ◽  
Guy Trambly de Laissardière
Keyword(s):  
Mean Field ◽  
Bilayer Graphene ◽  
Real Space ◽  
Localized States ◽  
Magic Angle ◽  
Experimental Realization ◽  
Hartree Fock ◽  
Large Size ◽  
Twisted Bilayer Graphene ◽  
Magnetic States

We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called ``magic angles’’ using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction UU that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effect is overestimated in the rescaled system, hinting at a complex interplay of flatness of the minibands close to the Fermi level and the spatial extent of the corresponding localized states. Our findings shed new light on perspectives for experimental realization of magnetic states in charge-neutral twisted bilayer graphene.

scholarly journals General continuum model for twisted bilayer graphene and arbitrary smooth deformations

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Leon Balents
Keyword(s):  
Continuum Model ◽  
Bilayer Graphene ◽  
Real Space ◽  
Lattice Deformation ◽  
Displacement Fields ◽  
Simple Derivation ◽  
Twisted Bilayer Graphene ◽  
General Continuum ◽  
The Continuum

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation – technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer graphene as well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

scholarly journals Real-Space Imaging of the Tailored Plasmons in Twisted Bilayer Graphene

2017 ◽  
Vol 119 (24) ◽  
Author(s):  
F. Hu ◽  
Suprem R. Das ◽  
Y. Luan ◽  
T.-F. Chung ◽  
Y. P. Chen ◽  
...  
Keyword(s):  
Bilayer Graphene ◽  
Real Space ◽  
Twisted Bilayer Graphene

scholarly journals Quantum Dot-like Plasmonic Modes in Twisted Bilayer Graphene Supercells

2D Materials ◽  
2021 ◽  
Author(s):  
T. Westerhout ◽  
Mikhail I Katsnelson ◽  
Malte Rösner
Keyword(s):  
Quantum Dots ◽  
Quantum Dot ◽  
Random Phase ◽  
System Size ◽  
High Energy ◽  
Bilayer Graphene ◽  
Real Space ◽  
Local Background ◽  
Twisted Bilayer Graphene ◽  
Twisting Angle

Abstract We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for $p_z$ electrons and their long-range Coulomb interaction. By disentangling low- and high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations to reliably describe the non-local background screening from the high-energy $s$, $p_x$, and $p_y$ electron states which we find to be independent of the bilayer stacking and thus of the twisting angle. The twist-dependent low-energy screening from $p_z$ states is subsequently added to obtain a full screening model. We use this modeling scheme to study plasmons in electron-doped twisted bilayer graphene supercells. We find that the finite system size yields discretized plasmonic levels, which are controlled by the system size, doping level, and twisting angle. This tunability together with atomic-like charge distributions of some of the excitations renders these plasmonic excitations remarkably similar to the electronic states in electronic quantum dots. To emphasize this analogy in the following we refer to these supercells as \emph{plasmonic quantum dots}. Based on a careful comparison to pristine AB-stacked bilayer graphene plasmons, we show that two kinds of plasmonic excitations arise, which differ in their layer polarization. Depending on this layer polarization the resulting plasmonic quantum dot states are either significantly or barely dependent on the twisting angle. Due to their tunability and their coupling to light, these plasmonic quantum dots form a versatile and promising platform for tailored light-matter interactions.

scholarly journals Correlation-Induced Insulating Topological Phases at Charge Neutrality in Twisted Bilayer Graphene

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuan Da Liao ◽  
Jian Kang ◽  
Clara N. Breiø ◽  
Xiao Yan Xu ◽  
Han-Qing Wu ◽  
...  
Keyword(s):  
Bilayer Graphene ◽  
Topological Phases ◽  
Charge Neutrality ◽  
Twisted Bilayer Graphene

scholarly journals Strange metal behavior of the Hall angle in twisted bilayer graphene

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
Rui Lyu ◽  
Zachary Tuchfeld ◽  
Nishchhal Verma ◽  
Haidong Tian ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Bilayer Graphene ◽  
Hall Angle ◽  
Twisted Bilayer Graphene

scholarly journals Correlated insulators in twisted bilayer graphene

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Ipsita Mandal ◽  
Jia Yao ◽  
Erich J. Mueller
Keyword(s):  
Bilayer Graphene ◽  
Twisted Bilayer Graphene
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