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van der Waals coefficients of the multi-layered MoS$_2$ with alkali metals

The van der Waals coefficients and the separation dependent retardation functions of the interactions between the atomically thin films of the multi-layered transition metal molybdenum disulfide (MoS$_2$) dichalcogenides with the alkali atoms are investigated. First, we determine the frequency-dependent dielectric permittivity and intrinsic carrier density values for different layers of MoS$_2$ by adopting various fitting models to the recently measured optical data reported by Yu and co-workers [Sci. Rep. {\bf 5}, 16996 (2015)] using spectroscopy ellipsometry. Then, dynamic electric dipole polarizabilities of the alkali atoms are evaluated very accurately by employing the relativistic coupled-cluster theory. We also demonstrate the explicit change in the above coefficients for different number of layers. These studies are highly useful for the optoelectronics, sensing and storage applications using layered MoS$_2$.