  Using an atomistic tight-binding model, we study the characteristics of a
Josephson junction formed by monolayers of MoS$_2$ sandwiched between Pb
superconducting electrodes. We derive and apply Green's function-based
formulation to compute the Josephson current in this system, as well as the
local density of states in the junction. Our analysis of diagonal and
off-diagonal components of the local density of states reveals the presence of
triplet superconducting correlations in the MoS$_2$ monolayers and
spin-polarized subgap (Andreev bound) states. Our formulation can be extended
to other systems where atomistic details and large scales are needed to obtain
accurate modeling of Josephson junction physics.
