  Since double resonance Raman (DRR) spectra are laser-energy dependent, the
first-principles calculations of DRR for two-dimensional materials are
challenging. Here, the DRR spectrum of monolayer MoTe$_2$ is calculated by
home-made program, in which we combine {\em ab-initio}
density-functional-theory calculations with the electron-phonon Wannier (EPW)
method. Within the fourth-order perturbation theory, we are able to quantify
not only the electron-photon matrix elements within the dipole approximation,
but also the electron-phonon matrix elements using the Wannier functions. The
reasonable agreement between the calculated and experimental Raman spectra is
achieved, in which we reproduce some distinctive features of transition metal
dichalcogenides (TMDCs) from graphene (for example, the dominant intervalley
process involving an electron or a hole). Furthermore, we perform an analysis
of the possible DRR modes over the Brillouin zone, highlighting the role of
low-symmetry points. Raman tensors for some DRR modes are given by first
principles calculations from which laser polarization dependence is obtained.
