Stokes and anti-Stokes double resonance Raman scattering in two-dimensional graphite

In this work, we discuss all possible double resonance processes which explain the observed features of the disorder-induced D band and its overtone, the $G^{\prime }$-band, in Stokes (S) and anti-Stokes (AS) Raman spectra of two-dimensional graphite. It is shown that the D band is composed by two peaks,which are not associated with resonances with the incident and scattered photons, but rather are related to whether the first scattering of an electron is by a phonon or by a defect. The model explains the experimental results concerning the frequency shift of the D and $G^{\prime }$ bands in the S and AS spectra, as well as the fact that the $G^{\prime }$ band is not centered at two times the center of the D-band frequency.