The low energy electronic band structure of bilayer graphene

McCann, Edward; Abergel, David; Falko, Vladimir

doi:10.1140/epjst/e2007-00229-1

Cited by 134 publications

(105 citation statements)

References 45 publications

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“…The double layer graphene system -the so-called bilayer graphene (BLG) -is now a subject of considerable interest due to its unusual properties, [1][2][3][4] dissimilar in large extent to those of the single layer graphene (SLG).…”

Section: Introductionmentioning

confidence: 99%

Electronic properties of a biased graphene bilayer

Castro

Новоселов

Морозов

et al. 2010

J. Phys.: Condens. Matter

299

235

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We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its 4-band and 2-band continuum approximations, and the 4-band model is shown to be always a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, either made out of SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point to understand the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, as the second-nearest-neighbor hopping energies t ′ (in-plane) and γ4 (inter-layer), and the on-site energy ∆.

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Section: Introductionmentioning

confidence: 99%

Electronic properties of a biased graphene bilayer

Castro

Новоселов

Морозов

et al. 2010

J. Phys.: Condens. Matter

299

235

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“…However, in single-layer graphene with charged impurities, the indirect interband processes contribute to the net THz conductivity σ only moderately due to a low density of states (DoS) near the band edges (except, possibly, for the case of the carrier interactions with artificial fairly large-size scatterers [22]) . The situation is remarkably different is the intrinsic graphene bilayers, where the electron-hole dispersion is gapless and almost parabolic [23]. With constant DoS near the band edges, the indirect interband radiative processes significantly contribute to the net radiation gain under the population inversion conditions.…”

mentioning

confidence: 99%

“…The interband conductivity of graphene bilayers due to the direct transitions is given by [19,23] Re…”

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confidence: 99%

Negative terahertz conductivity in disordered graphene bilayers with population inversion

Svintsov

Otsuji

Mitin

et al. 2015

Applied Physics Letters

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The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the direct interband transitions). In the graphene bilayer structures on high-κ substrates with point charged defects, these transitions almost fully compensate the losses due to the intraband (Drude) absorption. We also demonstrate that the indirect interband contribution to the THz conductivity in a graphene bilayer with the extended defects (such as the charged impurity clusters, surface corrugation, and nanoholes) can surpass by several times the fundamental limit associated with the direct interband transitions and the Drude conductivity. These predictions can affect the strategy of the graphene-based THz laser implementation.The absence of a band gap in the atomically thin carbon structures,such as graphene and graphene bilayers, enables their applications in different terahertz (THz) and infrared devices [1][2][3][4]. One of the most challenging and promising problems is the creation of the graphenebased THz lasers [5][6][7]. These lasers are expected to operate at room temperature, particularly, in the 6-10 THz range, where the operation of III-V quantum cascade lasers is hindered by the optical phonons [8]. Recent pump-probe spectroscopy experiments confirm the possibility of the coherent radiation amplification in the optically pumped graphene [9][10][11][12][13][14][15][16], enabled by a relatively long-living interband population inversion [17]. As opposed to optically pumped graphene lasers, graphenebased injection lasers are expected to operate in the continuous mode, with the interband population inversion maintained by the electron and hole injection from the n-and p-type contacts [18]. A single pumped graphene sheet as the gain medium provides the maximum radiation amplification coefficient corresponding to the quantity 4πσ Q /c = πα = 2.3%, where σ Q = e 2 /4 is the universal optical conductivity of a single graphene layer, e is the electron charge, is the Planck constant and α ≃ 1/137 is the fine-structure constant [17]. The THz

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“…Experimental observations 26,27,38,39 as well as theoretical studies [23][24][25][40][41][42] have demonstrated that applying an electrostatic field perpendicular to the BLG plane forms an energy asymmetry between the two layers of graphene and consequently alters its bandstructure. In Sec.…”

Section: Gate Voltage and Electrostatic Screeningmentioning

confidence: 99%

“…This enhancement is a result of the electric-field-induced energy asymmetry in BLG structures. Essentially, a vertical electric field in a metal-oxide-graphene geometry, creates an energy asymmetry between the two parallel layers of BLG [23][24][25] . The energy asymmetry changes the bandstructure of BLG, which in turn alters its optical properties significantly 26,27 .…”

Section: Introductionmentioning

confidence: 99%

Voltage tunable plasmon propagation in dual gated bilayer graphene

Farzaneh

Rakheja

2017

Journal of Applied Physics

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In this paper, we theoretically investigate plasmon propagation characteristics in AB and AA stacked bilayer graphene (BLG) in the presence of energy asymmetry due to an electrostatic field oriented perpendicularly to the plane of the graphene sheet. We first derive the optical conductivity of BLG using the Kubo formalism incorporating energy asymmetry and finite electron scattering. All results are obtained for room temperature (300K) operation. By solving Maxwell's equations in a dual gate device setup, we obtain the wavevector of propagating plasmon modes in the transverse electric (TE) and transverse magnetic (TM) directions at terahertz frequencies. The plasmon wavevector allows us to compare the compression factor, propagation length, and the mode confinement of TE and TM plasmon modes in bilayer and monolayer graphene sheets and also study the impact of material parameters on plasmon characteristics. Our results show that the energy asymmetry can be harnessed to increase the propagation length of TM plasmons in BLG. AA stacked BLG shows a larger increase in propagation length than AB stacked BLG; conversely, it is very insensitive to the Fermi level variations. Additionally, the dual gate structure allows independent modulation of the energy asymmetry and the Fermi level in BLG, which is advantageous for reconfiguring plasmon characteristics post device fabrication.

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The low energy electronic band structure of bilayer graphene

Cited by 134 publications

References 45 publications

Electronic properties of a biased graphene bilayer

Electronic properties of a biased graphene bilayer

Negative terahertz conductivity in disordered graphene bilayers with population inversion

Voltage tunable plasmon propagation in dual gated bilayer graphene

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