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Register a new userTheory of double-resonant Raman spectra in graphene: intensity and line shape of defect-induced and two-phonon bands
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We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D$, 2D and $2D$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal.
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By computing the double-resonant Raman scattering cross-section completely from first principles and including electron-electron interaction at the $GW$ level, we unravel the dominant contributions for the double-resonant 2D-mode in bilayer graphene. We show that, in contrast to previous works, the so-called inner processes are dominant and that the 2D-mode lineshape is described by three dominant resonances around the $K$ point. We show that the splitting of the TO phonon branch in $Gamma-K$ direction, as large as 12 cm$^{-1}$ in $GW$ approximation, is of great importance for a thorough description of the 2D-mode lineshape. Finally, we present a method to extract the TO phonon splitting and the splitting of the electronic bands from experimental data.
Broadening of the Raman scattering (RS) spectra was studied in monolayer graphene samples irradiated with various dose of ions followed by annealing of radiation damage at different temperatures. It is shown that the width {Gamma} (full width at half maximum, FWHM) of three main RS lines (G-, D-, and 2D) increases linearly with increase of the density of irradiation-induced point defects N d as {Delta}{Gamma} = m N d . The slope m of the linear dependencies is the same for one-phonon emitting G-line and D-line, and almost double for two-phonon emitting 2D-line. It is also shown that the width of D-line {Gamma} D for all samples is larger than one half of the width of 2D-line {Gamma} 2D , which shows that in the case of D-line, elastic electron scattering on point defects leads to an additional decreasing the lifetime of the emitted phonon. Theoretical model of the width of D-line in disordered graphene is developed which explains the experimental observations and allows to determine the numerical coefficient in the in-plane transverse optic phonon dispersion in graphene.
The line shape of the double-resonant $2D$ Raman mode in bilayer graphene is often considered to be characteristic for a certain laser excitation energy. Here, in a joint experimental and theoretical study, we analyze the dependence of the double-resonant Raman scattering processes in bilayer graphene on the electronic broadening parameter $gamma$. We demonstrate that the ratio between symmetric and anti-symmetric scattering processes sensitively depends on the lifetime of the electronic states, explaining the experimentally observed variation of the complex $2D$-mode line shape.
The Raman 2D line of graphene is widely used for device characterization and during device fabrication as it contains valuable information on e.g. the direction and magnitude of mechanical strain and doping. Here we present systematic asymmetries in the 2D line shape of exfoliated graphene and graphene grown by chemical vapor deposition. Both graphene crystals are fully encapsulated in van der Waals heterostructures, where hexagonal boron nitride and tungsten diselenide are used as substrate materials. In both material stacks, we find very low doping values and extremely homogeneous strain distributions in the graphene crystal, which is a hall mark of the outstanding electronic quality of these samples. By fitting double Lorentzian functions to the spectra to account for the contributions of inner and outer processes to the 2D peak, we find that the splitting of the sub-peaks, $6.6 pm 0.5$ cm$^{-1}$(hBN-Gr-WSe2) and $8.9 pm 1.0$ cm$^{-1}$ (hBN-Gr-hBN), is significantly lower than the values reported in previous studies on suspended graphene.
We present electronic structure calculations of twisted double bilayer graphene (TDBG): A tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles calculations, we find that TDBG is semiconducting with a band gap that depends on the twist angle, that can be tuned by an external electric field. The gap is consistent with TDBG symmetry and its magnitude is related to surface effects, driving electron transfer from outer to inner layers. The surface effect competes with an energy upshift of localized states at inner layers, giving rise to the peculiar angle dependence of the band gap, which reduces at low angles. For these low twist angles, the TDBG develops flat bands, in which electrons in the inner layers are localized at the AA regions, as in twisted bilayer graphene.
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