  Resonance Raman scattering, which probes electrons, phonons and their
interplay in crystals, is extensively used in two-dimensional materials. Here
we investigate Raman modes in MoSe$_2$ at different laser excitation energies
from 2.33 eV down to the near infrared 1.16 eV. The Raman spectrum at 1.16 eV
excitation energy shows that the intensity of high-order modes is strongly
enhanced if compared to the first-order phonon modes intensity due to resonance
effects with the MoSe$_2$ indirect band gap. By comparing the experimental
results with the two-phonon density of states calculated with density
functional theory, we show that the high-order modes originate mostly from
two-phonon modes with opposite momenta. In particular, we identify the momenta
of the phonon modes that couple strongly with the electrons to produce the
resonance process at 1.16 eV, while we verify that at 2.33 eV the two-phonon
modes lineshape compares well with the two-phonon density of state calculated
over the entire Brillouin Zone. We also show that, by lowering the crystal
temperature, we actively suppress the intensity of the resonant two-phonon
modes and we interpret this as the result of the increase of the indirect band
gap at low temperature that moves our excitation energy out of the resonance
condition.
