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A Comprehensive Multiphonon Spectral Analysis in MoS2

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.