A comprehensive multiphonon spectral analysis in MoS ₂

We present a comprehensive multiphonon Raman and complementary infrared analysis for bulk and monolayer MoS 2 . 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 Γ Brillouin zone (BZ) points. The attribution of about 80 transitions of up to fifth order processes are proposed in the low temperature (95 K) resonant Raman spectrum measured with excitation energy of 1.96 eV, which is slightly shifted in energy from the A exciton. We propose that the main contributions come from four phonons: A 1g (M), E 1 2g (M 1 ), E 2 2g (M 1 ) (TA′ (M)) and E 2 2g (M 2 ) (LA′ (M)). The last three are single degenerate phonons at M with an origin of the E 1 2g ( Γ ) and E 2 2g ( Γ ) 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 longitudinal acoustic (LA(M)) mode can not be considered with the above four phonons. Although minor, contributions from K point and possibly Γ -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 explain the lower part of the band, previously attributed to 2LA(M), as being due to a van Hove singularity between K and M. The higher part, previously attributed exclusively to the A 2u ( Γ ) phonon, is mostly due to the LA and LA′ phonons at M. For the monolayer MoS 2 the second-order phonon processes from the M and Γ BZ points are also analyzed and are discussed within similar framework to that of the bulk.