Probing combinations of acoustic phonons in Mo S 2 by intervalley double-resonance Raman scattering

In this work, we present measurements of the temperature dependence of the resonance Raman spectra of $\\mathrm{Mo}{\\mathrm{S}}_{2}$ in two-dimensional and bulk forms, performed to identify the processes related to different combinations of two acoustic phonons involved in the intervalley scattering. The resonance Raman spectra of samples of different thicknesses (single layer, bilayer, trilayer, and bulk) were measured near the resonance with the $A$ excitonic transition and at different temperatures. Measurements of the Raman spectra of bulk $\\mathrm{Mo}{\\mathrm{S}}_{2}$ were performed using several laser energies across the resonances with the $A$ and $B$ excitonic transitions. Based on the electronic and vibrational structures of the samples with different thicknesses and the evolution of the bands as a function of the laser excitation energy and temperature, we propose correct assignments to the Raman bands appearing at approximately 380, 395, and $405\\phantom{\\rule{0.16em}{0ex}}\\mathrm{c}{\\mathrm{m}}^{\\ensuremath{-}1}$. According to our measurements and data analysis, the peaks at 380, 395, and $405\\phantom{\\rule{0.16em}{0ex}}\\mathrm{c}{\\mathrm{m}}^{\\ensuremath{-}1}$ correspond to the combinations of 2TA around the K point, LA and TA phonons around the M point, and LA and out-of-plane acoustic (ZA) phonons around the M point, respectively. This work sheds light on the double-resonance processes of $\\mathrm{Mo}{\\mathrm{S}}_{2}$ and how it is related to the electronic structure of this material. The results presented here establish the assignment and the scattering mechanism for some two-phonon and double-resonance Raman bands whose origins were still a matter of debate in the literature. It can also be an important basis to explain the double-resonance processes in other transition-metal dichalcogenides since we present the fundamental electron scattering mechanism near the resonance with the $A$ and $B$ excitonic transitions, and how it is affected by thermal effects.