  We theoretically investigate the possibility of achieving a superconducting
state in transition-metal dichalcogenide bilayers through intercalation, a
process previously and widely used to achieve metallization and superconducting
states in novel superconductors. For the Ca-intercalated bilayers MoS$_2$ and
WS$_2$, we find that the superconducting state is characterized by an
electron-phonon coupling constant larger than $1.0$ and a superconducting
critical temperature of $13.3$ and $9.3$ K, respectively. These results are
superior to other predicted or experimentally observed two-dimensional
conventional superconductors and suggest that the investigated materials may be
good candidates for nanoscale superconductors. More interestingly, we proved
that the obtained thermodynamic properties go beyond the predictions of the
mean-field Bardeen--Cooper--Schrieffer approximation and that the calculations
conducted within the framework of the strong-coupling Eliashberg theory should
be treated as those that yield quantitative results.
