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We study the second-order Raman process of mono- and few-layer MoTe$_2$, bycombining {\em ab initio} density functional perturbation calculations withexperimental Raman spectroscopy using 532, 633 and 785 nm excitation lasers.The calculated electronic band structure and the density of states show thatthe electron-photon resonance process occurs at the high-symmetry M point inthe Brillouin zone, where a strong optical absorption occurs by a logarithmicVan-Hove singularity. Double resonance Raman scattering with inter-valleyelectron-phonon coupling connects two of the three inequivalent M points in theBrillouin zone, giving rise to second-order Raman peaks due to the M pointphonons. The predicted frequencies of the second-order Raman peaks agree withthe observed peak positions that cannot be assigned in terms of a first-orderprocess. Our study attempts to supply a basic understanding of the second-orderRaman process occurring in transition metal di-chalcogenides (TMDs) and mayprovide additional information both on the lattice dynamics and opticalprocesses especially for TMDs with small energy band gaps such as MoTe$_2$ orat high laser excitation energy.

Double resonance Raman modes in mono- and few-layer MoTe$_2$