DUV Double-Resonant Raman Spectra and Interference Effect in Graphene: First-Principles Calculations

We calculate double-resonance Raman (DRR) spectra of monolayer graphene by first-principles density functional calculation, for wide laser excitation energies from the near-infrared (1.58 eV) to the deep-ultraviolet (DUV, 5.41 eV) region. When laser excitation energy, $E_L$, goes into the DUV region, Raman peak wavenumber for G ${}^{\ast }$ band switches from red-shift to blue-shift and for 2D ${}^{\prime }$ band switches from red-shift to constant, in contrast to the continuous blue-shift of G ${}^{\prime }$ band. Raman intensity of the three bands generally decreases with increasing $E_L$, except for $E_L$ around 4.08 eV where Raman intensity diverges due to van Hove singularity of electron density of states. The combined two-phonon modes change with $E_L$ for both G ${}^{\prime }$ and G ${}^{\ast }$ bands (e.g., from 2LO to 2TO and back to 2LO for G ${}^{\prime }$ and from LA + LO/TO to TA + LO/TO for G ${}^{\ast }$) but remain 2LO for 2D ${}^{\prime }$ band. Further, the dominant DRR scattering process of G ${}^{\prime }$ band changes from the electron-hole ( $eh$ or $he$) scattering processes to the $ee$ scattering processes as $E_L$ goes into the DUV region, since the Dirac energy bands become asymmetric between $\pi$ and ${\pi }^{\ast }$ band that suppresses the $eh$ process and the Raman intensity. Another factor to suppress the Raman intensity is the quantum interference effect between four scattering processes ( $eh,he,ee,hh$) which changes from constructive to destructive interference and finally to no interference with increasing $E_L$. We calculate $E_L$-dependent Raman tensor of the three bands and polarized Raman spectra, which further support the interference effect. The calculated results are directly compared and consistent with the experimental results.