Electronic structure and optical properties of twisted bilayer graphene calculated via time evolution of states in real space

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
H. Anh Le ◽  
V. Nam Do
Keyword(s):  
Optical Properties ◽  
Electronic Structure ◽  
Time Evolution ◽  
Bilayer Graphene ◽  
Real Space ◽  
Twisted Bilayer Graphene

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 Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling

2018 ◽  
Vol 115 (27) ◽  
pp. 6928-6933 ◽  
Author(s):  
Wei Yao ◽  
Eryin Wang ◽  
Changhua Bao ◽  
Yiou Zhang ◽  
Kenan Zhang ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Graphene Layer ◽  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Double Resonance ◽  
Interlayer Coupling ◽  
Bilayer Graphene ◽  
Lattice Vector ◽  
Graphene Layers ◽  
Twisted Bilayer Graphene

The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far research in heterostructures has been focused on commensurate superlattices with a long-ranged Moiré period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm−1. Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism—that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures.

scholarly journals Electronic structure of bilayer graphene: A real-space Green’s function study

2007 ◽  
Vol 75 (8) ◽  
Author(s):  
Z. F. Wang ◽  
Qunxiang Li ◽  
Haibin Su ◽  
Xiaoping Wang ◽  
Q. W. Shi ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Green’S Function ◽  
Green's Function ◽  
Bilayer Graphene ◽  
Real Space ◽  
Function Study

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 Minibands in twisted bilayer graphene probed by magnetic focusing

2020 ◽  
Vol 6 (16) ◽  
pp. eaay7838 ◽  
Author(s):  
A. I. Berdyugin ◽  
B. Tsim ◽  
P. Kumaravadivel ◽  
S. G. Xu ◽  
A. Ceferino ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Magnetic Fields ◽  
Long Range ◽  
Electron Scattering ◽  
Low Temperatures ◽  
Ballistic Transport ◽  
Bilayer Graphene ◽  
Degree Of Freedom ◽  
Magnetic Focusing ◽  
Twisted Bilayer Graphene

Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here, we use magnetic focusing to probe narrowbands in graphene bilayers twisted at ~2°. Their minibands are found to support long-range ballistic transport limited at low temperatures by intrinsic electron-electron scattering. A voltage bias between the layers causes strong minivalley splitting and allows selective focusing for different minivalleys, which is of interest for using this degree of freedom in frequently discussed valleytronics.

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 Twisted Bilayer Graphene: Low‐Energy Physics, Electronic and Optical Properties

2019 ◽  
pp. 177-231 ◽  
Author(s):  
Gonçalo Catarina ◽  
Bruno Amorim ◽  
Eduardo V. Castro ◽  
Eduardo V. Castro ◽  
Eduardo V. Castro ◽  
...  
Keyword(s):  
Optical Properties ◽  
Bilayer Graphene ◽  
Low Energy ◽  
Electronic And Optical Properties ◽  
Twisted Bilayer Graphene ◽  
Energy Physics

scholarly journals Electronic structure and quantum transport in twisted bilayer graphene with resonant scatterers

2020 ◽  
Vol 101 (24) ◽  
Author(s):  
Omid Faizy Namarvar ◽  
Ahmed Missaoui ◽  
Laurence Magaud ◽  
Didier Mayou ◽  
Guy Trambly de Laissardière
Keyword(s):  
Electronic Structure ◽  
Quantum Transport ◽  
Bilayer Graphene ◽  
Twisted Bilayer Graphene
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