Electric-field-induced rich magneto-absorption spectra of ABC-stacked trilayer graphene

Lin, Yi; Lin, Chiun-Yan; Chang, C. P.; Lin, Min Pei

doi:10.1039/c5ra15045k

Cited by 8 publications

(22 citation statements)

References 28 publications

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“…74 Several theoretical studies on the magnetooptical properties are performed for AAA-and ABC-stacked trilayer graphenes. 71 On the other hand, a thorough systematic study on the magnetooptical properties of ABA-stacked trilayer graphene is absent up to now. 67,68 The above-mentioned ffiffiffiffiffi ffi B 0 p dependence and selection rule are suitable for N-layer AAA graphene.…”

Section: Introductionmentioning

confidence: 99%

Rich magneto-absorption spectra of AAB-stacked trilayer graphene

Shih

Chang

et al. 2016

Phys. Chem. Chem. Phys.

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A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.

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Section: Introductionmentioning

confidence: 99%

Rich magneto-absorption spectra of AAB-stacked trilayer graphene

Shih

Chang

et al. 2016

Phys. Chem. Chem. Phys.

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“…An electric field can separate the two partially flat bands and trigger a new kind of optical channels responsible for a gap transition [104,106]. Under a magnetic field, intergroup and intragroup excitation channels among well-behaved LLs comprise the main part of the absorption spectrum [140,[167][168][169], in which the absorption peaks show the twin-peak structure because the LL energy spectrum is asymmetric about E F = 0 [168,169]. Moreover, it is interesting to study the quantization effects of any two constant-energy loops in the sombrero-shaped structure, where the quantized energies of the LLs are proportional or inversely proportional to the magnetic field strength [120,140,141].…”

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confidence: 99%

“…By using an exact diagonalization method, the eigenvalues and eigenfunctions of the Hamiltonian matrix are efficiently solved. The developed model could be further used to understand the other essential material properties by combing the single-and many-particle 8 theories, such as optical spectra and electronic excitations [152,155,168,169,[181][182][183][184][185][186][187]. On the other hand, the effective-mass approximation is frequently adopted to comprehend the electronic and optical properties.…”

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confidence: 99%

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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“…By using an exact diagonalization method, the eigenvalues and eigenfunctions of the Hamiltonian matrix are efficiently solved. The developed model can be further used to understand other essential material properties by combining the single-and many-particle theories, such as optical spectra and electronic excitations [158,159,162,175,176,[190][191][192][193][194][195][196]. On the other hand, the effective mass approximation is frequently adopted to comprehend the electronic and optical properties.…”

Section: Introductionmentioning

confidence: 99%

“…An electric field can separate the two partially flat bands and trigger a new kind of optical channel responsible for a gap transition [110,112]. Under a magnetic field, the intergroup and intragroup excitation channels among wellbehaved LLs comprise the main part of the absorption spectrum [146,[174][175][176], in which the absorption peaks show a twin-peak structure because the LL energy spectrum is asymmetric about = E 0 F [175,176]. Moreover, it is interesting to study the quantization effects of any two constant energy loops in the sombrero-shaped structure, where the quantized energies of the LLs are proportional or inversely proportional to the magnetic field strength [126,146,147].…”

Section: Introductionmentioning

confidence: 99%