Low-Energy Landau Level Spectrum in ABC-Stacked Trilayer Graphene

Ho, Ching Hong; Tsai, Sing Jyun; Chen, Rong Bin; Chiu, Yu Huang; Lin, Ming–Fa

doi:10.1166/jnn.2011.4145

Cited by 14 publications

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“…[12][13][14][15] Electronic states in a uniform perpendicular magnetic field B = B 0 ẑ are evolved to quantized Landau levels (LLs). [65][66][67][68][69][70][71][72][73][74][75][76] It should be noted that such LLs in AA-stacked graphenes are separated from each other by tens of meV, 33,66 while such LLs in AB-and ABC-stacked graphenes are confined in a narrow energy range of 10 meV around E F = 0; 67,69,73,75,76,84 their energy differences can be verified by quantum transport experiments. 4,138,139 On the other hand, the massive fermions in bilayer graphene give rise to quantized LL energies ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nðn À 1Þ p B 0 .…”

Section: Introductionmentioning

confidence: 94%

“…[73][74][75] Owing to the periodicity of the Peierls phase, the primitive unit cell becomes an enlarged rectangle unit cell along the x-direction (the armchair direction), as indicated in Fig. [73][74][75] Owing to the periodicity of the Peierls phase, the primitive unit cell becomes an enlarged rectangle unit cell along the x-direction (the armchair direction), as indicated in Fig.…”

Section: Monolayer Graphenementioning

confidence: 99%

“…[35][36][37][38][39] In ABC systems, there is always one pair of weakly dispersive bands with surface-localized states near the Fermi level, 39,41,[43][44][45] and peculiar sombrero-shaped dispersion bands near the energy of the vertical nearestneighboring interlayer interaction. 33,34,37,39,49,50,53,56,[63][64][65][66][67][68][69][70][71][72][73][74][75][76]81,84,[107][108][109] In the presence of a uniform perpendicular electric field, the Dirac cones in AA-stacked graphenes are preserved, 33,34,65 while only a rigid shift from E F = 0 takes place. The above-mentioned stackingdependent electronic structures have been experimentally verified by infrared optical spectroscopy [101][102][103][104][105] and angle-resolved photoemission spectroscopy.…”

Section: Introductionmentioning

confidence: 99%

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Magneto-electronic properties of multilayer graphenes

Lin

et al. 2015

Phys. Chem. Chem. Phys.

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This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.

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Section: Introductionmentioning

confidence: 94%

Section: Monolayer Graphenementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magneto-electronic properties of multilayer graphenes

Lin

et al. 2015

Phys. Chem. Chem. Phys.

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“…uniform/modulated magnetic fields [124,125,150], modulated electric fields and composite fields [151]. This is suitable for multi-layer graphene [126,128,143,144] and bulk graphite [255,256] with arbitrary stacking configurations. The most important interlayer atomic interactions and external fields are simultaneously taken into account without the need to treat either of them as a perturbation term.…”

Section: Introductionmentioning

confidence: 99%

Introduction

Lin¹,

Do²,

Huang³

et al. 2017

Optical Properties of Graphene in Magnetic and Electric Fields

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“…This model can be utilized in cases where many kinds of external fields are applied, e.g., uniform/modulated magnetic fields [118,119]; [144], modulated electric fields, and composite fields [145]. It is suitable for multi-layer graphene [120,122,137,138] and bulk graphites [332,333], with arbitrary stacking configurations. Most important interlayer atomic interactions and external fields are simultaneously taken into account without the need for treating either of them as a perturbation term.…”

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Optical Properties of Graphene in Magnetic and Electric Fields

Lin

Huang

et al. 2017

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Optical properties of graphene are explored by using the generalized tight-binding model. The main features of spectral structures, the form, frequency, number and intensity, are greatly enriched by the complex relationship among the interlayer atomic interactions, the magnetic quantization and the Coulomb potential energy. Absorption spectra have shoulders, asymmetric peaks and logarithmic peaks, coming from the band-edge states of parabolic dispersions, the constant-energy loops and the saddle points, respectively. The initial forbidden excitation region is only revealed in even-layer AA stacking systems. Optical gaps and special structures can be generated by an electric field. The delta-function-like structures in magneto-optical spectra, which present the single, twin and double peaks, are associated with the symmetric, asymmetric and splitting Landau-level energy spectra, respectively. The single peaks due to the non-tilted Dirac cones exhibit the nearly uniform intensity. The AAB stacking possesses more absorption structures, compared to the other stackings. The diverse magneto-optical selection rules are mainly determined by the well-behaved, perturbed and undefined Landau modes. The frequent anti-crossings in the magneticand electric-field-dependent energy spectra lead to the increase of absorption peaks and the reduced intensities. Part of theoretical calculations are consistent with the 1 arXiv:1603.02797v2 [physics.comp-ph] 19 Jul 2016 experimental measurements, and the others need further detailed examinations.Graphene is a 2D material made up of hexagonal carbon lattices [1,2]. Since mono-and few-layer graphene sheets were first fabricated in 2004 [1,2], low-dimensional graphenerelated systems have been a great interest to experimental and theoretical studies. The stacking orders of graphene sheets include the essential sequences of AA [3,4], AB [5-9], ABC [5,[8][9][10][11] stackings. While the AA stacking configuration has only been artificially made from intercalated graphite compounds, the AB and ABC configurations are the common orders in natural graphite, respectively, with their estimated volume fractions: 80 % and 14 % [15,16]. The rest parts ∼ 6% consist of haphazardly stacked graphene sheets, called turbostratic configuration [17][18][19]. Few-layer graphene desired with a specific stacking configuration can be exfoliated from highly orientated pyrolytic graphite [1,2], and chemically and electrochemically reduced from graphene oxide [20][21][22][23][24][25][26][27]. Nevertheless, chemical vapor deposition method has the advantage of producing large-scale size of highquality graphene sheets. Recently, large area of graphene with high mobility and highly symmetric configurations, e.g., AA, AB and ABC, have been found in CVD-grown samples [28][29][30][31][32][33][34][35][36][37][38][39][40]. The improved quality is adequate for research experiments and industry applications [41][42][43][44][45][46][47][48][49][50]. In addition, the AAB stacking and intermediate bilayer configurations, with r...

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Low-Energy Landau Level Spectrum in ABC-Stacked Trilayer Graphene

Cited by 14 publications

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Magneto-electronic properties of multilayer graphenes

Magneto-electronic properties of multilayer graphenes

Introduction

Optical Properties of Graphene in Magnetic and Electric Fields

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