Electronic states and Landau levels in graphene stacks

Guinea, F.; Neto, A. H. Castro; Peres, N. M. R.

doi:10.1103/physrevb.73.245426

Cited by 626 publications

(306 citation statements)

References 32 publications

(46 reference statements)

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“…However, the stacking sequence of FLG is experimentally found to exert pronounced influence on the electronic band structure [150], which are compared in Figure 10(c,d), and thus the electrical properties of FLG with different stacking sequences are expected to be distinct to some extent. For example, the Bernal trilayer is viewed as a semimetal with electrically tunable band overlap [120,169–171], while the rhombohedral trilayer is predicted to be a semiconductor with a band gap that can be electrically tuned [153,169,170]. Moreover, the application of a certain electric field can finally open larger band gap in the latter than that in the former [153,172].…”

Section: The Structure Of Graphenementioning

confidence: 99%

Structure of graphene and its disorders: a review

Gao

Lee

et al. 2018

Science and Technology of Advanced Materials

487

187

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Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp3-defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.

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Section: The Structure Of Graphenementioning

confidence: 99%

Structure of graphene and its disorders: a review

Gao

Lee

et al. 2018

Science and Technology of Advanced Materials

487

187

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“…The electronic structure of trilayer graphene (TLG) has been predicted to consist of both massless single-layer-graphene-like and massive bilayer-graphene-like Dirac subbands [4][5][6][7] , which should result in new types of mesoscopic and quantum Hall phenomena. However, the low mobility exhibited by TLG devices on conventional substrates has led to few experimental studies 8,9 .…”

mentioning

confidence: 99%

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

et al. 2011

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The physics of Dirac fermions in condensed-matter systems has received extraordinary attention following the discoveries of two new types of quantum Hall effect in single-layer and bilayer graphene [1][2][3] . The electronic structure of trilayer graphene (TLG) has been predicted to consist of both massless single-layer-graphene-like and massive bilayer-graphene-like Dirac subbands [4][5][6][7] , which should result in new types of mesoscopic and quantum Hall phenomena. However, the low mobility exhibited by TLG devices on conventional substrates has led to few experimental studies 8,9 . Here we investigate electronic transport in high-mobility (>100,000 cm Bernal-or ABA-stacked TLG (Fig. 1b) is an intriguing material to study Dirac physics and the quantum Hall effect (QHE) because of its unique band structure, which, in the simplest approximation, consists of massless single-layer-graphene (SLG)-like and massive bilayer graphene (BLG)-like subbands at low energy (Fig. 1c;. The energies of the Landau levels (LLs) for massless charge carriers depend on the square root of the magnetic field √ B (refs 1, 2,11-13), whereas for massive charge carriers they depend linearly on B (refs 3,11,12,14). Therefore, the LLs from these two different subbands in TLG should cross at some finite fields, resulting in accidental LL degeneracies at the crossing points. However, one of the main challenges so far to observe the QHE in TLG has been its low mobility on SiO 2 substrates 8,9 . To overcome this problem, we use hexagonal boron nitride (hBN) single crystals 15 as local substrates, which have been shown to reduce carrier scattering in graphene devices 16 (See Methods and Supplementary Information for fabrication). Substrate-supported devices also enable us to reach higher carrier density than suspended samples 17 , which is necessary for the observation of the LL crossings. Figure 1e,f shows the resistivity and conductivity of a TLG device at zero magnetic field. The resistivity at the Dirac peak exhibits a strong temperature dependence, which in SLG is a strong indication of high device quality 18,19 . In addition, we also observe a doublepeak structure at low temperatures (Fig. 1e). This double-peak structure is probably due to the band overlap that occurs in TLG when all SWMcC parameters are included in the tight-binding calculation of its band structure, as we show below. The field-effect mobility of this device reaches 110,000 cm 2 V −1 s −1 at 300 mK at densities as high as 6 × 10 11 cm −2 . This mobility value is two orders of magnitude higher than previously reported values for supported TLG (refs 8,9) and comparable to suspended samples 17,19 . The low disorder and high mobility enable us to probe LL crossings of Dirac fermions through the measurement of Shubnikov-de Haas oscillations (SdHOs). Figure 2a shows longitudinal resistivity ρ xx as a function of 1/B, for a carrier density n = −4.4 × 10 12 cm −2 . At low B (below ∼1 T), there are a number of oscillations characterized by broad minima separated by relatively n...

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“…Similar to the monolayer, bilayer graphene shows a zero-gap band structure at the Dirac point. However, the crossing bands are not linear but parabolic describing electrons with a nite mass [9,13,14,42] (cf. Fig.…”

Section: Absorption Spectramentioning

confidence: 99%

Relaxation Dynamics in Graphene

Malić

Knorr

2013

Graphene and Carbon Nanotubes

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In this thesis, the relaxation dynamics of nonequilibrium carriers in graphene is investigated. Based on the density matrix approach, the interaction of carriers with light, phonons and electrons is theoretically modelled. The resulting time-, momentum-, and angle-resolved simulation of the carrier dynamics enables the interpretation of recent experimental observations. Typically, the carrier relaxation has been accessed via high-resolution pump-probe experiments. Common to all studies is a bi-exponential decay of the pump-induced differential transmission (DT) spectrum. The fast decay component in the range of few tens of femtoseconds is assigned to an ultrafast Coulomb-dominated carrier redistribution towards a hot Fermi-Dirac distribution, whereas the slower decay component in the range of a picosecond reflects the equilibration between the electron and the phonon system. However, many studies report a zero-crossing after the initial decay in the transient DT spectrum, where the second decay component characterizes the recovering of the DT signal. In very good agreement with recent pump-probe experiment performed by the group of Prof. Manfred Helm (Helmholtz-Zentrum Dresden-Rossendorf), a microscopic explanation for the occurrence of transient negative differential transmission in graphene is found, where a detailed interplay of intraand interband absorption processes on the transient DT in graphene is investigated. In particular, phonon-assisted intraband processes are shown to lead to an enhanced absorption giving rise to the experimentally observed zero-crossing from positive to negative DT signals.In collaboration with the group of Prof. Theodore B. Norris (Michigan University, USA), theoretical studies combined with ultrafast time-resolved THz spectroscopy were performed to systematically investigate the hot-carrier dynamics in an array of graphene samples. The theory calculates explicitly the time-dependent response of the system to a THz probe pulse. The calculations reveal that the observed dynamics can be accounted for qualitatively without including any fitting parameters, phenomenological models or extrinsic effects. Specifically, the hot-carrier dynamics are governed by the coupling of extraordinarily efficient carrier-carrier and carrier-phonon interactions. Furthermore, the theory demonstrates that the simple Drude model is insufficient to fully account for the THz interactions.Beside pump-probe studies, the thesis presents the absorption spectra of mono-and bilayer graphene including the impact of the fully momentum-dependent optical and Coulomb matrix elements. In agreement with recent experiments, the absorbance of graphene is characterized by a frequency-independent value in the near-infrared spectral region and a pronounced peak in the ultraviolet region resulting from interband transition. In contrast to the linear band structure of graphene, the energy dispersion of bilayer graphene exhibits four parabolic bands resulting in interesting optical features: The absorbance exhibits in...

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Electronic states and Landau levels in graphene stacks

Cited by 626 publications

References 32 publications

Structure of graphene and its disorders: a review

Structure of graphene and its disorders: a review

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

Relaxation Dynamics in Graphene

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