Theory of double-resonant Raman spectra in graphene: Intensity and line shape of defect-induced and two-phonon bands

By P. Venezuela, M. Lazzeri, F. Mauri. 2011

521 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/86cbffc074a073c8713d9d02f05b09d3221d99c2

How researchers see this paper

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In Atomic and Molecular Physics, and Optics

1. Zhenhua Ni
2. O. Frank
3. Lukás Novotný
4. V. Valev
5. Ryan Beams
6. V. Holý
7. D. Hooper
8. Ladislav Kavan

In Materials Chemistry

1. Zhangting Wu
2. Zhenhua Ni
3. Lukás Novotný
4. Ryan Beams
5. Z. Zafar
6. Xing Wu
7. Z. Shi
8. O. Frank

Citations in the corpus

• Raman characterization of defects and dopants in graphene (2015, background): “The D and D′ bands can also give rise to overtones and combination modes, thereby resulting in additional symmetry-breaking modes in the Raman spectra [50, 51].”
• Evolution of Raman spectra in nitrogen doped graphene (2013, background): “The intensity of 2D peak is strongly depended on the electron/hole scattering rate (2C), which is affected by lattice defects as well as charge carrier doping [33].”
• Spectroscopic investigation of defects in two-dimensional materials (2016, background): “increases, the phonons involved in the double resonant process move away from K, and their frequencies become higher [93].”
• Interaction between graphene and copper substrate: The role of lattice orientation (2014, background): “FWHM(2D) increases and I(2D) decreases upon both p- and n-doping mainly due to electronelectron interactions, and also electron-phonon coupling strength (expressed as a dimensionless parameter λ), which increases to a small extent upon doping [62, 65].”