Two-dimensional analysis of the double-resonant 2D Raman mode in bilayer   graphene
  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. 
Felix Herziger, Matteo Calandra, Paola Gava, Patrick May, Michele   Lazzeri, Francesco Mauri, Janina Maultzsch
cond-mat.mes-hall