Dirac electrons in a dodecagonal graphene quasicrystal

Quantum states of quasiparticles in solids are dictated by symmetry. We have experimentally demonstrated quantum states of Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystalline order was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°. We grew the graphene quasicrystal up to a millimeter scale on a silicon carbide surface while maintaining the single rotation angle over an entire sample and successfully isolated the quasicrystal from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cones replicated with the 12-fold rotational symmetry were observed in angle-resolved photoemission spectra, which revealed anomalous strong interlayer coupling with quasi-periodicity. Our study provides a way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.

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

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1720865115 ◽

2018 ◽

Vol 115 (27) ◽

pp. 6928-6933 ◽

Cited By ~ 55

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.

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Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133916 ◽

1990 ◽

Vol 48 (2) ◽

pp. 64-65

Author(s):

L. Reimer ◽

R. Oelgeklaus

Keyword(s):

Fourier Transform ◽

Energy Loss ◽

Electron Energy ◽

Rotational Symmetry ◽

Mean Free Path ◽

Single Scattering ◽

Specimen Thickness ◽

Two Dimensional ◽

Image Position ◽

Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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Unfolding energy spectra of double-periodicity two-dimensional systems: Twisted bilayer graphene and MoS2 on graphene

Physical Review Materials ◽

10.1103/physrevmaterials.2.010801 ◽

2018 ◽

Vol 2 (1) ◽

Cited By ~ 4

Author(s):

Yu-ichiro Matsushita ◽

Hirofumi Nishi ◽

Jun-ichi Iwata ◽

Taichi Kosugi ◽

Atsushi Oshiyama

Keyword(s):

Bilayer Graphene ◽

Energy Spectra ◽

Two Dimensional ◽

Twisted Bilayer Graphene

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New stable two dimensional silicon carbide nanosheets

Journal of Alloys and Compounds ◽

10.1016/j.jallcom.2021.159201 ◽

2021 ◽

Vol 868 ◽

pp. 159201

Author(s):

Qun Wei ◽

Ying Yang ◽

Guang Yang ◽

Xihong Peng

Keyword(s):

Silicon Carbide ◽

Two Dimensional

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Stability and superconductivity of Ca-intercalated bilayer blue phosphorene

Physical Chemistry Chemical Physics ◽

10.1039/d0cp05984f ◽

2021 ◽

Author(s):

Artur Durajski ◽

Kamil Skoczylas ◽

Radoslaw Szczesniak

Keyword(s):

Superconducting State ◽

Potential Application ◽

Recent Experiment ◽

Superconducting Devices ◽

Bilayer Graphene ◽

Two Dimensional ◽

Twisted Bilayer Graphene ◽

Blue Phosphorene

Superconductivity attracts much interest in two-dimensional compounds due to their potential application in nano-superconducting devices. Inspired by a recent experiment reporting the superconducting state in twisted bilayer graphene, here, based...

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General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2006.1694 ◽

2006 ◽

Vol 462 (2073) ◽

pp. 2695-2713 ◽

Cited By ~ 5

Author(s):

Cyril Dubus ◽

Ken Sekimoto ◽

Jean-Baptiste Fournier

Keyword(s):

Blood Cell ◽

Red Blood Cell ◽

Triangular Lattice ◽

Soft Matter ◽

Rotational Symmetry ◽

Three Dimensions ◽

Nearest Neighbour ◽

Two Dimensional ◽

Biological Physics ◽

Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

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Generation of a Two-Dimensional Silicon Carbide Lattice

Advances in X-Ray Analysis ◽

10.1007/978-1-4684-7633-0_12 ◽

1966 ◽

pp. 142-151

Author(s):

R. L. Prickett ◽

R. L. Hough

Keyword(s):

Silicon Carbide ◽

Two Dimensional

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Evidence for Interlayer Coupling and Moiré Periodic Potentials in Twisted Bilayer Graphene

Physical Review Letters ◽

10.1103/physrevlett.109.186807 ◽

2012 ◽

Vol 109 (18) ◽

Cited By ~ 124

Author(s):

Taisuke Ohta ◽

Jeremy T. Robinson ◽

Peter J. Feibelman ◽

Aaron Bostwick ◽

Eli Rotenberg ◽

...

Keyword(s):

Interlayer Coupling ◽

Bilayer Graphene ◽

Periodic Potentials ◽

Twisted Bilayer Graphene

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Waterproof molecular monolayers stabilize 2D materials

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1909500116 ◽

2019 ◽

Vol 116 (42) ◽

pp. 20844-20849 ◽

Cited By ~ 4

Author(s):

Cong Su ◽

Zongyou Yin ◽

Qing-Bo Yan ◽

Zegao Wang ◽

Hongtao Lin ◽

...

Keyword(s):

Transition Metal ◽

Theoretical Analysis ◽

2D Materials ◽

Transition Metal Dichalcogenides ◽

Water Molecules ◽

Two Dimensional ◽

Ambient Conditions ◽

Molecular Monolayers ◽

Metal Dichalcogenides ◽

Van Der Waals Materials

Two-dimensional van der Waals materials have rich and unique functional properties, but many are susceptible to corrosion under ambient conditions. Here we show that linear alkylamines n-CmH2m+1NH2, with m = 4 through 11, are highly effective in protecting the optoelectronic properties of these materials, such as black phosphorus (BP) and transition-metal dichalcogenides (TMDs: WS2, 1T′-MoTe2, WTe2, WSe2, TaS2, and NbSe2). As a representative example, n-hexylamine (m = 6) can be applied in the form of thin molecular monolayers on BP flakes with less than 2-nm thickness and can prolong BP’s lifetime from a few hours to several weeks and even months in ambient environments. Characterizations combined with our theoretical analysis show that the thin monolayers selectively sift out water molecules, forming a drying layer to achieve the passivation of the protected 2D materials. The monolayer coating is also stable in air, H2 annealing, and organic solvents, but can be removed by certain organic acids.

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