scholarly journals Landau levels for graphene layers in noncommutative plane

2021 ◽  
pp. 2150087
Author(s):  
Lucas Sourrouille
Keyword(s):  
Energy Spectrum ◽  
Bilayer Graphene ◽  
Landau Levels ◽  
Graphene Layers ◽  
Zero Modes ◽  
Commutative Space ◽  
Noncommutative Plane

Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.

Electronic and optical properties of monolayer and bilayer graphene

2010 ◽  
Vol 368 (1932) ◽  
pp. 5445-5458 ◽  
Author(s):  
Y. H. Ho ◽  
J. Y. Wu ◽  
Y. H. Chiu ◽  
J. Wang ◽  
M. F. Lin
Keyword(s):  
Optical Properties ◽  
Bilayer Graphene ◽  
Landau Levels ◽  
Optical Measurements ◽  
Monolayer Graphene ◽  
Zero Field ◽  
Electronic And Optical Properties ◽  
Graphene Layers ◽  
Lower Pair ◽  
Dependent Absorption

The electronic and optical properties of monolayer and bilayer graphene are investigated to verify the effects of interlayer interactions and external magnetic field. Monolayer graphene exhibits linear bands in the low-energy region. Then the interlayer interactions in bilayers change these bands into two pairs of parabolic bands, where the lower pair is slightly overlapped and the occupied states are asymmetric with respect to the unoccupied ones. The characteristics of zero-field electronic structures are directly reflected in the Landau levels. In monolayer and bilayer graphene, these levels can be classified into one and two groups, respectively. With respect to the optical transitions between the Landau levels, bilayer graphene possesses much richer spectral features in comparison with monolayers, such as four kinds of absorption channels and double-peaked absorption lines. The explicit wave functions can further elucidate the frequency-dependent absorption rates and the complex optical selection rules. These numerical calculations would be useful in identifying the optical measurements on graphene layers.

Zero Modes & Fractional Charge in Bilayer Graphene

2011 ◽  
Author(s):  
J. C. Martinez ◽  
M. B. A. Jalil ◽  
S. G. Tan ◽  
Jisoon Ihm ◽  
Hyeonsik Cheong
Keyword(s):  
Bilayer Graphene ◽  
Fractional Charge ◽  
Zero Modes

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.

Selective growth of monolayer and bilayer graphene patterns by a rapid growth method

Nanoscale ◽  
2019 ◽  
Vol 11 (14) ◽  
pp. 6727-6736 ◽  
Author(s):  
Maddumage Don Sandeepa Lakshad Wimalananda ◽  
Jae-Kwan Kim ◽  
Ji-Myon Lee
Keyword(s):  
Surface Treatment ◽  
Rapid Growth ◽  
Bilayer Graphene ◽  
Selective Growth ◽  
Catalytic Surface ◽  
Graphene Layers ◽  
Plasma Treatments ◽  
Growth Method

Selective surface treatment of a catalytic surface by different plasma treatments to control the number of graphene layers.

scholarly journals On the Thermodynamic Properties of the Spinless Duffin-Kemmer-Petiau Oscillator in Noncommutative Plane

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Zhi Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Wei Zhang
Keyword(s):  
Functional Analysis ◽  
Energy Spectrum ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Eigenvalue ◽  
Noncommutative Space ◽  
Analysis Method ◽  
Physical Systems ◽  
Noncommutative Plane ◽  
Noncommutative Parameter

The Duffin-Kemmer-Petiau oscillator for spin 0 particle in noncommutative plane is analyzed and the energy eigenvalue of the system is obtained by employing the functional analysis method. Furthermore, the thermodynamic properties of the noncommutative DKP oscillator are investigated via numerical method and the influence of noncommutative space on thermodynamic functions is also discussed. We show that the energy spectrum and corresponding thermodynamic functions of the considered physical systems depend explicitly on the noncommutative parameterθwhich characterizes the noncommutativity of the space.

THE HALL CONDUCTIVITY OF A DOPED GRAPHENE IN A QUANTIZING MAGNETIC FIELD

2012 ◽  
Vol 26 (28) ◽  
pp. 1250188 ◽  
Author(s):  
MIKHAIL B. BELONENKO ◽  
ANASTASIA V. PAK ◽  
ALEXANDER V. ZHUKOV ◽  
ROLAND BOUFFANAIS
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Energy Spectrum ◽  
Applied Magnetic Field ◽  
Electron Energy Spectrum ◽  
Landau Levels ◽  
Adsorbed Atom ◽  
Doped Graphene ◽  
Quantizing Magnetic Field ◽  
Different Characteristics

In this paper we study the electron energy spectrum corresponding to Landau levels in doped graphene when an external magnetic field is applied in the direction normal to the graphene planar sheet. The derived dispersion relation for the electrons in the doped graphene allows us to determine the dependence of the electrical conductivity on the applied magnetic field. This relationship between electrical conductivity and applied magnetic field is further analyzed for different characteristics of the impurities; specifically the potential of hybridization and the energy of the adsorbed atom.

An analytical approach for the energy spectrum and optical properties of gated bilayer graphene

RSC Advances ◽  
2014 ◽  
Vol 4 (61) ◽  
pp. 32117-32126 ◽  
Author(s):  
Cheng-Peng Chang
Keyword(s):  
Optical Properties ◽  
Energy Spectrum ◽  
Matrix Element ◽  
Absorption Spectra ◽  
Analytical Approach ◽  
Bilayer Graphene ◽  
Wave Functions ◽  
Dipole Matrix Element ◽  
Exact Energy

An analytical approach is developed to access the exact energy spectrum, wave functions, dipole matrix element (Mfi) and absorption spectra (A(ω)) of gated Bernal bilayer graphene.

Landau levels in a simple hexagonal bilayer graphene

2008 ◽  
Vol 372 (3) ◽  
pp. 292-298 ◽  
Author(s):  
Y.H. Lai ◽  
C.P. Chang ◽  
J.H. Ho ◽  
C.H. Ho ◽  
M.F. Lin
Keyword(s):  
Bilayer Graphene ◽  
Landau Levels

scholarly journals Moire Is Different

2021 ◽  
Vol 13 (1) ◽  
pp. 50
Author(s):  
Wenyuan Shi
Keyword(s):  
Electronic Structures ◽  
Tight Binding ◽  
Physical Property ◽  
Large Change ◽  
Bilayer Graphene ◽  
Dirac Fermion ◽  
Dirac Fermions ◽  
Graphene Layers ◽  
Flat Bands ◽  
Twisted Bilayer Graphene

Graphene, as the thinnest material ever found, exhibits unconventionally relativistic behaviour of Dirac fermions. However, unusual phenomena (such as superconductivity) arise when stacking two graphene layers and twisting the bilayer graphene. The relativistic Dirac fermion in graphene has been widely studied and understood, but the large change observed in twisted bilayer graphene (TBG) is intriguing and still unclear because only van der Waals force (vdW) interlayer interaction is added from graphene to TBG and such a very weak interaction is expected to play a negligible role. To understand such dramatic variation, we studied the electronic structures of monolayer, bilayer and twisted bilayer graphene. Twisted bilayer graphene creates different moiré patterns when turned at different angles. We proposed tight-binding and effective continuum models and thereby drafted a computer code to calculate their electronic structures. Our calculated results show that the electronic structure of twisted bilayer graphene changes significantly even by a tiny twist. When bilayer graphene is twisted at special “magic angles”, flat bands appear. We examined how these flat bands are created, their properties and the relevance to some unconventional physical property such as superconductivity. We conclude that in the nanoscopic scale, similar looking atomic structures can create vastly different electronic structures. Like how P. W. Anderson stated that similar looking fields in science can have differences in his article “More is Different”, similar moiré patterns in twisted bilayer graphene can produce different electronic structures.

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