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Insights into vibrational and electronic properties of MoS$_2$ using Raman, photoluminescence and transport studies

We review vibrational and electronic properties of single and a few layer MoS$_2$ relevant to understand their resonant and non-resonant Raman scattering results. In particular, the optical modes and low frequency shear and layer breathing modes show significant dependence on the number of MoS$_2$ layers. Further, the electron doping of the MoS$_2$ single layer achieved using top-gating in a field effect transistor renormalizes the two optical modes A$_{1g}$ and E$^1_{2g}$ differently due to symmetry-dependent electron-phonon coupling. The issues related to carrier mobility, the Schottky barrier at the MoS$_2$-metal contact pads and the modifications of the dielectric environment are addressed. The direct optical transitions for single layer-MoS$_2$ involve two excitons at K-point in the Brillouin zone and their stability with temperature and pressure has been reviewed. Finally, the Fermi-level dependence of spectral shift for a quasiparticle, called trion, has been discussed.