Flat band electrons and interactions in rhombohedral trilayer graphene

Wang, Hao; Gao, Jin-Hua; Zhang, Fuchun

doi:10.1103/physrevb.87.155116

Cited by 20 publications

(18 citation statements)

References 55 publications

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“…Few-layer graphene with specific stacking configurations, e.g. AA [78][79][80], AB [81][82][83][84][85][86][87][88][89][90][91][92][93], ABC [93][94][95][96][97][98][99] and AAB [64], are predicted to display unique electronic energy dispersions. This new material holds great promise for the development of next-generation electronic and optoelectronic nanodevices [41-47, [50][51][52][53][54][55][56] because the electronic and optical properties can be flexibly tuned by the application of external fields [64][65][66][67][68][69][70][71][72][73][74] as well as changes to the geometric structures and dopants [115][116][117][118][119]…”

Section: Introductionmentioning

confidence: 99%

“…Few-layer ABC-stacked graphene is a semimetal [93][94][95][96][97][98][99]. The electronic structure is characterized by one pair of partially flat subbands near = E 0 F , and pairs of sombrero-shaped subbands near the energy of the vertical atomic interactions between the nearest-neighboring layers [93][94][95][96][97][98][99].…”

Section: Introductionmentioning

confidence: 99%

“…The electronic structure is characterized by one pair of partially flat subbands near = E 0 F , and pairs of sombrero-shaped subbands near the energy of the vertical atomic interactions between the nearest-neighboring layers [93][94][95][96][97][98][99]. Contributed by the surface-localized states [97][98][99], the partially flat subbands give rise to a prominent peak in the density of states (DOS) and play an important role in the low-frequency optical spectrum [110,112]. 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].…”

Section: Introductionmentioning

confidence: 99%

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Introduction

Lin¹,

Do²,

Huang³

et al. 2017

Optical Properties of Graphene in Magnetic and Electric Fields

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Introduction

Lin¹,

Do²,

Huang³

et al. 2017

Optical Properties of Graphene in Magnetic and Electric Fields

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“…The subtle difference in stacking order of the two systems results in dramatic distinctions in their band structures and electronic properties [7][8][9][10][11][12][13][14]. Very recently, the r-TLG has attracted much attention because of its low-energy flat bands, which are predicted to result in many strongly correlated phenomena [7,[23][24][25][26], such as spontaneous gap formation, superconductivity, and ferromagnetism. However, the STM fails to identify the stacking order for the graphene multilayers with the layer number N 3.…”

Section: Introductionmentioning

confidence: 99%

Direct probing of the stacking order and electronic spectrum of rhombohedral trilayer graphene with scanning tunneling microscopy

Xu¹,

Yin²,

Qiao³

et al. 2015

Phys. Rev. B

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Recently, rhombohedral trilayer graphene (r-TLG) has attracted much attention because of its low-energy flat bands, which are predicted to result in many strongly correlated phenomena. However, there has been a need for more experimental evidence for these flat bands in the r-TLG, since the supporting substrates usually have strong destructive effects on the low-energy band structure of graphene systems. Here, we demonstrate that it is possible to directly probe the stacking order and electronic spectrum of the r-TLG on a graphite surface with scanning tunneling microscopy around a monoatomic step edge of the top graphene layer. The tunneling spectra of the r-TLG exhibit four adjacent peaks, which are generated by the low-energy flat bands, flanking the charge neutrality point. Based on these spectra, the true energy gap and the energy gap at the K point of the r-TLG are determined as about 9 and 23 meV, respectively. The observed features are well reproduced by a low-energy effective Hamiltonian.

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“…The electronic structure is characterized by one pair of partially flat subbands near E F = 0, and pairs of sombreroshaped subbands near the energy of the vertical atomic interactions between nearestneighboring layers [87][88][89][90][91][92][93]. Contributed by the surface-localized states [91][92][93], the partially flat subbands give rise to a prominent peak in DOS and plays an important role in the low-frequency optical spectrum [104,106]. 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].…”

mentioning

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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Flat band electrons and interactions in rhombohedral trilayer graphene

Cited by 20 publications

References 55 publications

Introduction

Introduction

Direct probing of the stacking order and electronic spectrum of rhombohedral trilayer graphene with scanning tunneling microscopy

Optical Properties of Graphene in Magnetic and Electric Fields

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