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ABSTRACT: The G-band Raman intensity is calculated for twisted bilayer graphene as a function of laser excitation energy based on the extended tight binding method. Here we explicitly consider the electron-photon and electron-phonon matrix elements of twisted bilayer graphene to calculate the resonance Raman intensity. The G-band Raman intensity is sensitive to the laser excitation energy and the twisting angle between the layers as a result of folding the electronic energy band structure. The Van Hove energy singularity, which is an electron transition energy between the conduction and valence bands, depends on n−m of the twisting vector (n,m). The relative intensity of the G band as a function of twisting vectors is presented, which should be useful for the experimental identification of the twisting angle.
Phys. Rev. B. 09/2012; 86(12).
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ABSTRACT: The G' (or 2D) Raman band of AB stacked bilayer graphene comes from a double resonance Raman (DRR) process and is composed of four peaks (P(11), P(12), P(21), and P(22)). In this work, the integrated areas (IA) of these four peaks are analyzed as a function of the laser power for different laser lines. We show that the dependence of the IA of each peak on temperature is different for each distinct laser excitation energy. This special dependence is explained in terms of the electron-phonon coupling and the relaxation of the photon-excited electron. In this DRR process, the electron is scattered by an iTO phonon from a K to an inequivalent K' point of the Brillouin zone. Here, we show that this electron relaxes while in the conduction band before being scattered by an iTO phonon due to the short relaxation time of the excited electron, and the carrier relaxation occurs predominantly by emitting a low-energy acoustic phonon. The different combinations of relaxation processes determine the relative intensities of the four peaks that give rise to the G' band. Some peaks show an increase of their IA at the expense of others, thereby making the IA of the peaks both different from each other and dependent on laser excitation energy and on power level. Also, we report that the IA of the G' mode excited at 532 nm, shows a resonance regime involving ZO' phonons (related to the interlayer breathing mode in bilayer graphene systems) in which a saturation of what we call the P(12) process occurs. This effect gives important information about the electron and phonon dynamics and needs to be taken into account for certain applications of bilayer graphene in the field of nanotechnology.
Nano Letters 05/2012; 12(6):2883-7. · 13.20 Impact Factor
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ABSTRACT: In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS(2), WSe(2), oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications.
Scientific Reports 01/2012; 2:1017.
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ABSTRACT: Bernal (ABA stacking order) and rhombohedral (ABC) trilayer graphene (3LG) are characterized by Raman spectroscopy. From a systematic experimental and theoretical analysis of the Raman modes in both of these 3LGs, we show that the G band, G' (2D) band, and the intermediate-frequency combination modes of 3LGs are sensitive to the stacking order of 3LG. The phonon wavevector q, that gives the double resonance Raman spectra is larger in ABC than ABA, which is the reason why we get the different Raman frequencies and their spectral widths for ABA and ABC 3LG. The weak electron-phonon interaction in ABC-stacked 3LG and the localized strain at the boundary between ABC- and ABA-stacked domains are clearly reflected by the softening of the G mode and the G' mode, respectively.
ACS Nano 10/2011; 5(11):8760-8. · 10.77 Impact Factor
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ABSTRACT: The double resonance Raman spectra of the overtone of the out-of-plane tangential optical (oTO) phonon and of combinations of the LO, ZO, and ZA phonons with one another are calculated for bilayer graphene. In the case of the bilayer graphene, these Raman peaks are observed in the energy region between 1600 and 1800 cm-1. We obtain results for both the fixed q=0 and the dispersive q=2k peaks of the overtones of the oTO phonon of bilayer graphene. We calculate the double resonance Raman spectra of the combination modes coming from the LO, iTO, LA, and iTA phonons in bilayer graphene. The calculated Raman peaks are compared with the experimental results.
Phys. Rev. B. 07/2011; 84(3).
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ABSTRACT: Electron energy-loss spectra of single double-walled carbon nanotubes (DWCNTs) were compared with calculated joint density of states (jDOSs) obtained by a simple tight-binding (STB) and an extended tight-binding (ETB) method. From the comparisons, interband transition energies of ETB calculations show better agreement with peak positions of the experimental spectra than those of STB results. From a further comparison among calculated jDOS, real and imaginary parts of a dielectric function and a loss function Im[-1/epsilon], it was confirmed that the peak energies in a spectrum of single DWCNTs are almost equal to those of the optical absorption spectrum epsilon(2).
Journal of electron microscopy 08/2008; 57(4):129-32. · 1.31 Impact Factor
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ABSTRACT: We theoretically investigate the dependence of exciton transition energies on dielectric constant of surrounding materials. We make a simple model for the relation between dielectric constant of environment and a static dielectric constant describing the effects of electrons in core states, $\sigma$ bonds and surrounding materials. Although the model is very simple, calculated results well reproduce experimental transition energy dependence on dielectric constant of various surrounding materials. Comment: 5pages, 4 figures
04/2007;
