  We present a comprehensive multiphonon Raman and complementary infrared
analysis for bulk and monolayer MoS2.For the bulk the analysis consists of
symmetry assignment from which we obtain a broad set of allowed second order
transitions at the high symmetry M,K and gamma Brillouin zone points. The
attribution of about 80 transitions of up to fifth order Raman processes are
proposed in the low temperature(95K)resonant Raman spectrum measured with the
excitation energy of 1.96 eV,which is slightly shifted from the A exciton. We
propose that the main contributions come from four
phonons:A1g(M),E12g(M2),E22g(M1)(TA'(M))and E22g (M2)(LA'(M)). The last three
are single degenerate phonons at M with an origin of the E12g(gamma)and
E22g(gamma)phonons. Among the four phonons, we identify in the resonant Raman
spectra all(but one) of the second order overtones,combination and difference
bands and many of the third order bands. Consistent with the expectation that
at the M point only combinations with the same inversion symmetry (g or u)are
Raman allowed, the contribution of combinations with the LA(M)phonon can not be
considered with the above four phonons. Although minor,contribution from K
point and possibly gamma point phonons are also evident. The "2LA
band",measured at ~460 cm-1 is reassigned.Supported by the striking similarity
between this band, measured under off resonant conditions, and recently
published two phonon density of states, we propose that the lower part of the
band,previously attributed to 2LA(M),is due to a van Hove singularity between K
and M. The higher part,previously attributed exclusively to the
A2u(gamma)phonon,is mostly due to the LA and LA' phonons at M. For the
monolayer MoS2, the second order phonon processes from M and gamma Brillouin
zone points are also analyzed and are discussed within similar framework to
that of the bulk.
