\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We present a G$_0$W calculation of the quasiparticle properties of $\rm{MoS_2}$ monolayer at $T=0$ considering the dynamical electron-electron interaction effect within random-phase-approximation (RPA). The calculations are carried out for an electron-doped slab of $\rm{MoS_2}$ monolayer using a minimal massive Dirac Hamiltonian and the quasi-two-dimensional nature of the Coulomb interaction in this system is taken into account considering a modified interaction of Keldysh type. Having calculated the real and imaginary parts of the retarded self-energy, we calculate the spectral function and discuss the impact of extrinsic variables such as the dielectric medium and the charge carrier density on the appearance and position of the quasiparticle peaks. We also report the results of the renormalization constant and the effective Fermi velocity calculations in a broad range of the coupling constant and carrier density. We show that the effective Fermi velocity obtained solving the self-consistent Dyson equation has an absolutely different behavior with the one found to form the on-shell approximation. Our results show that the nonlocal screening of the monolayer crystal tends to stabilize the Fermi liquid picture in $\rm{MoS_2}$ monolayer and that the interaction strength parameter of this system is a multivariable function of the coupling constant, carrier density and also the screening length of the crystal.
\end{document}