Resonance effects in the Raman scattering of mono- and few layers MoSe$_2$

Using resonant Raman scattering spectroscopy with 25 different laser lines, we describe the Raman scattering spectra of mono- and multi-layers 2H-molybdenum diselenide (MoSe$_2$) as well as the different resonances affecting the most pronounced features. For high-energy phonons, both A- and E- symmetry type phonons present resonances with A and B excitons of MoSe$_2$ together with a marked increase of intensity when exciting at higher energy, close to the C exciton energy. We observe symmetry dependent exciton-phonon coupling affecting mainly the low-energy rigid layer phonon modes. The shear mode for multilayer displays a pronounced resonance with the C exciton while the breathing mode has an intensity that grows with the excitation laser energy, indicating a resonance with electronic excitations at energies higher than that of the C exciton.