  We present complete calculations of the two-phonon Raman bands of bilayer
graphene, including all overtone and combination modes, within a
density-functional tight-binding model. Based on our results, we assign
unambiguously the observed two-phonon Raman bands to two-phonon modes, thus
resolving the existing controversies. In particular, we show that both overtone
and combination modes have essential contribution to the 2D band, bringing
about specific modifications of the band shape. We argue that a mid-range
two-phonon Raman band, previously assigned to the 2ZO mode, should be assigned
to the TOZO' mode. We find that the Raman band, usually assigned to the LOLA
mode, has significant contribution from the TOZO mode. The predicted Raman
bands can be used for assignment of the observed ones in the Raman spectra of
bilayer graphene for the needs of sample characterization for future
technological applications.

Mesoscale and Nanoscale Physics