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Landau Quantization in Graphene Monolayer, Bernal Bilayer, and Bernal Trilayer on Graphite Surface  [PDF]
Long-Jing Yin,Si-Yu Li,Jia-Bin Qiao,Jia-Cai Nie,Lin He
Physics , 2015, DOI: 10.1103/PhysRevB.91.115405
Abstract: Electronic properties of surface areas decoupled from graphite are studied using scanning tunnelling microscopy and spectroscopy. We show that it is possible to identify decoupled graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface according to their tunnelling spectra in high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap, ~35 meV, in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split into two valley-polarized quartets polarized on each layer. In the decoupled Bernal trilayer, we find that both massless and massive Dirac fermions coexist and its low-energy band structure can be described quite well by taking into account only the nearest-neighbor intra- and interlayer hopping parameters. A strong correlation between the Fermi velocity of the massless Dirac fermions and the effective mass of the massive Dirac fermions is observed in the trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers.
Interface Landau levels in graphene monolayer-bilayer junction  [PDF]
Mikito Koshino,Takeshi Nakanishi,Tsuneya Ando
Physics , 2010, DOI: 10.1103/PhysRevB.82.205436
Abstract: Electronic structure of graphene monolayer-bilayer junction in a magnetic field is studied within an effective-mass approximation. The energy spectrum is characterized by interface Landau levels, i.e., the locally flat bands appearing near the boundary region, resulting in a series of characteristic peaks in the local density of states. Their energies are independent of boundary types such as zigzag or armchair. In the atomic scale, the local density of states shows a Kekul\'{e} pattern due to the valley mixing in the armchair boundary, while does not in the zigzag boundary.
Landau level degeneracy and quantum Hall effect in a graphite bilayer  [PDF]
Edward McCann,Vladimir I. Fal'ko
Physics , 2005, DOI: 10.1103/PhysRevLett.96.086805
Abstract: We derive an effective two-dimensional Hamiltonian to describe the low energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase $2\pi$. Its high-magnetic-field Landau level spectrum consists of almost equidistant groups of four-fold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, $\sigma_{xy}(N)$, which exhibits plateaus at integer values of $4e^{2}/h$ and has a ``double'' $8e^{2}/h$ step between the hole and electron gases across zero density, in contrast to $(4n+2)e^{2}/h$ sequencing in a monolayer.
Nanoindentation of a circular sheet of bilayer graphene  [PDF]
M. Neek-Amal,F. M. Peeters
Physics , 2011, DOI: 10.1103/PhysRevB.81.235421
Abstract: Nanoindentation of bilayer graphene is studied using molecular dynamics simulations. We compared our simulation results with those from elasticity theory as based on the nonlinear F\"{o}ppl-Hencky equations with rigid boundary condition. The force deflection values of bilayer graphene are compered to those of monolayer graphene. Young's modulus of bilayer graphene is estimated to be 0.8 TPa which is close to the value for graphite. Moreover, an almost flat bilayer membrane at low temperature under central load has a 14$%$ smaller Young's modulus as compared to the one at room temperature.
Spatially resolving unconventional interface Landau quantization in a graphene monolayer-bilayer planar junction  [PDF]
Wei Yan,Si-Yu Li,Long-Jing Yin,Jia-Bin Qiao,Jia-Cai Nie,Lin He
Physics , 2015,
Abstract: Graphene hybrid planar structures consisting of two regions with different quantum Hall (QH) states exhibit unusual transport properties1-5, originating from chiral edge states equilibration at the interface of the two different regions6. Here we present a sub-nanometre-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of a monolayer-bilayer graphene planar junction in the QH regime. The atomically well-defined interface of such a junction allows us to spatially resolve the interface electronic properties. Around the interface, we detect Landau quantization of massless Dirac fermions, as expected in graphene monolayer, below the charge neutrality point Nc of the junction, whereas unexpectedly, only Landau quantization of massive Dirac fermions, as expected in graphene bilayer, is observed above the Nc. The observed unconventional interface Landau quantization arises from the fact that the quantum conductance across the interface is solely determined by the minimum filling factors (number of edge modes) in the graphene monolayer and bilayer regions of the junction6,7.
Systematic Investigation of the Intrinsic Channel Properties and Contact Resistance of Monolayer and Multilayer Graphene FET  [PDF]
Kosuke Nagashio,Tomonori Nishimura,Koji Kita,Akira Toriumi
Physics , 2010, DOI: 10.1143/JJAP.49.051304
Abstract: The intrinsic channel properties of monolayer and multilayer graphene were systematically investigated as a function of layer number by the exclusion of contact resistance using four-probe measurements. We show that the continuous change in normalized sheet resistivity from graphite to a bilayer graphene is governed by one unique property, i.e., the band overlap, which markedly increases from 1 meV for a bilayer graphene to 11 meV for eight layers and eventually reaches 40 meV for graphite. The monolayer graphene, however, showed a deviation in temperature dependence due to a peculiar linear dispersion. Additionally, contact resistivity was extracted for the case of typical Cr/Au electrodes. The observed high contact resistivity, which varies by three orders of magnitude (from ~103 to 106 Ohm micron), might significantly mask the outstanding performance of the monolayer graphene channel, suggesting its importance in future research.
Electron-Phonon Interactions in Bilayer Graphene: A First Principles Approach  [PDF]
K. M. Borysenko,J. T. Mullen,X. Li,Y. G. Semenov,J. M. Zavada,M. Buongiorno Nardelli,K. W. Kim
Physics , 2010,
Abstract: Density functional perturbation theory is used to analyze electron-phonon interaction in bilayer graphene. The results show that phonon scattering in bilayer graphene bears more resemblance with bulk graphite than monolayer graphene. In particular, electron-phonon scattering in the lowest conduction band is dominated by six lowest (acoustic and acoustic-like) phonon branches with only minor contributions from optical modes. The total scattering rate at low/moderate electron energies can be described by a simple two-phonon model in the deformation potential approximation with effective constants Dac $\approx$ 15 eV and Dop $\approx 2.8 \times 108$ eV/cm for acoustic and optical phonons, respectively. With much enhanced acoustic phonon scattering, the low field mobility of bilayer graphene is expected to be significantly smaller than that of monolayer graphene.
Electron Tunneling in Monolayer and Bilayer Graphene  [PDF]
Di Wu,Weiqiang Chen,Fu-Chun Zhang
Physics , 2008,
Abstract: Electron's tunneling through potential barrier in monolayer and bilayer graphene lattices is investigated by using full tight-binding model. Emphasis is placed on the resonance tunneling feature and inter-valley scattering probability. It is shown that normal incidence transmission probabilities for monolayer and bilayer graphene exhibit different properties. Our calculation indicates that valleytronics in graphene systems may be detected, generated and controlled by changing the structure parameters of the external electric potential.
Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene  [PDF]
Andreas Sinner,Klaus Ziegler
Physics , 2011, DOI: 10.1103/PhysRevB.84.233401
Abstract: The DC conductivity of monolayer and bilayer graphene is studied perturbatively for different types of disorder. In the case of monolayer, an exact cancellation of logarithmic divergences occurs for all disorder types. The total conductivity correction for a random vector potential is zero, while for a random scalar potential and a random gap it acquires finite corrections. We identify the diagrams which are responsible for these corrections and extrapolate the finite contributions to higher orders which gives us general expressions for the conductivity of weakly disordered monolayer graphene. In the case of bilayer graphene, a cancellation of all contributions for all types of disorder takes place. Thus, the minimal conductivity of bilayer graphene turns out to be very robust against disorder.
Electron-Phonon Interactions in Graphene, Bilayer Graphene, and Graphite  [PDF]
Cheol-Hwan Park,Feliciano Giustino,Marvin L. Cohen,Steven G. Louie
Physics , 2008, DOI: 10.1021/nl801884n
Abstract: Using first-principles techniques, we calculate the renormalization of the electron Fermi velocity and the vibrational lifetimes arising from electron-phonon interactions in doped bilayer graphene and in graphite and compare the results with the corresponding quantities in graphene. For similar levels of doping, the Fermi velocity renormalization in bilayer graphene and in graphite is found to be approximately 30% larger than that in graphene. In the case of bilayer graphene, this difference is shown to arise from the interlayer interaction. We discuss our findings in the light of recent photoemission and Raman spectroscopy experiments.
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