Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Ho, Ching Hong; Ho, Yen-Hung; Chiu, Yu-Huang; Chen, Yueh-Nan; Lin, Mingyao

doi:10.1016/j.aop.2010.11.004

Cited by 16 publications

(12 citation statements)

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“…Charge ordering phenomena occurring upon symmetry breaking are important in solids as they give rise to new current and spin flow patterns in promising materials such as organic conductors [1], multilayered graphene [2] and transition metal oxides [3]. The possibility to investigate the microscopic steps through which such ordering transition occurs gives also the opportunity to speculate on more general aspects of critical phenomena.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…Although the photoinduced electronic temperature far exceeds the critical value, the charge-density wave is preserved until the lattice is sufficiently distorted to induce the phase transition. Combining this result with ab initio electronic structure calculations, we identified the Peierls origin of multiple charge-density waves in a three-dimensional system for the first time.Charge ordering phenomena occurring upon symmetry breaking are important in solids as they give rise to new current and spin flow patterns in promising materials such as organic conductors [1], multilayered graphene [2] and transition metal oxides [3]. The possibility to investigate the microscopic steps through which such ordering transition occurs gives also the opportunity to speculate on more general aspects of critical phenomena.…”

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confidence: 99%

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Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid

Mansart

Cottet

Penfold

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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The effect of dimensionality on materials properties has become strikingly evident with the recent discovery of graphene. Charge ordering phenomena can be induced in one dimension by periodic distortions of a material's crystal structure, termed Peierls ordering transition. Charge-density waves can also be induced in solids by strong coulomb repulsion between carriers, and at the extreme limit, Wigner predicted that crystallization itself can be induced in an electrons gas in free space close to the absolute zero of temperature. Similar phenomena are observed also in higher dimensions, but the microscopic description of the corresponding phase transition is often controversial, and remains an open field of research for fundamental physics. Here, we photoinduce the melting of the charge ordering in a complex three-dimensional solid and monitor the consequent charge redistribution by probing the optical response over a broad spectral range with ultrashort laser pulses. Although the photoinduced electronic temperature far exceeds the critical value, the charge-density wave is preserved until the lattice is sufficiently distorted to induce the phase transition. Combining this result with ab initio electronic structure calculations, we identified the Peierls origin of multiple charge-density waves in a three-dimensional system for the first time.ultrafast broadband spectroscopy | electron-lattice interactions | optical spectral weight C harge ordering phenomena occurring upon symmetry breaking are important in solids as they give rise to current and spin flow patterns in promising materials such as organic conductors (1), multilayered graphene (2) and transition metal oxides (3). The possibility to investigate the microscopic steps through which such ordering transition occurs also gives the opportunity to speculate on more general aspects of critical phenomena. Chargedensity waves (CDWs) (4, 5), sandpile automata (6), and Josephson arrays (7) have been investigated in relation to the scale invariance of self-organized critical phenomena (8), of which avalanches are dramatic manifestations (9). In one dimension, Peierls demonstrated that at low temperature an instability can be induced by the coupling between carriers and a periodic lattice distortion. Such an instability triggers a charge ordering phenomenon and a metal-insulator phase transition, called Peierls transition, occurs (10). Like for Bardeen-Cooper-Schrieffer (BCS) superconductors, such an electron-phonon interaction-driven transition is expected to be second order (10). Although this situation is fairly established in monodimensional organic materials (11), increased hybridization leading to higher dimensionality of a solid perturbs this scenario and makes the assessment of the microscopic origin of charge localization phenomena more difficult (12)(13)(14).Contrary to other low-dimensional CDW (15) systems studied so far by time-resolved spectroscopies (16-19), Lu 5 Ir 4 Si 10 presents a complex three-dimensional structure with several substructures suc...

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Section: Pacs Numbersmentioning

confidence: 99%

mentioning

confidence: 99%

Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid

Mansart

Cottet

Penfold

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…For example, interactions lead to a marginal Fermi liquid behavior in neutral single layer graphene, 5,6 and to brokensymmetry ordered states in bilayers. [7][8][9][10][11][12][13][14][15] The recent surge of interest in ABC stacked trilayer graphene [16][17][18][19][20][21][22][23][24][25][26][27] motivates theoretical studies of the electron interaction induced instabilities that are expected when these structures are weakly disordered. Instabilities are favored in ABC trilayers by extremely flat crossing 2 of a single-pair of bands at the neutral system Fermi level, and by exchange energy frustration associated with mometum-space textures in the valence band wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

Gapped broken symmetry states in ABC-stacked trilayer graphene

Jung

MacDonald

2013

Phys. Rev. B

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We use a self-consistent Hartree-Fock approximation with realistic Coulomb interactions for π-band electrons to explore the possibility of broken symmetry states in weakly disordered ABC stacked trilayer graphene. The competition between gapped and gapless broken symmetry states, and normal states is studied by comparing total energies. We find that gapped states are favored and that, unlike the bilayer case, gapless nematic broken symmetry states are not metastable. Among the gapped states the layer antiferromagnetic state is favored over anomalous and spin Hall states.

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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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Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Cited by 16 publications

References 62 publications

Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid

Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid

Gapped broken symmetry states in ABC-stacked trilayer graphene

Optical Properties of Graphene in Magnetic and Electric Fields

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