  The strong coupling between lattice modes and charges which leads to the
formation of charge density waves in materials such as the transition-metal
dichalcogenides may also give rise to superconductivity in the same materials,
mediated by the same exciton or phonon modes that dominate the charge ordered
state. Such a superconducting phase has recently been observed for example in
TiSe2, both upon intercalation with Copper and in the pristine material under
pressure. Here we investigate the interplay of exciton formation and
electron-phonon coupling within a simplified model description. We find that
the combined exciton-phonon modes previously suggested to drive the charge
density wave instability in TiSe2 are also responsible for the pairing of
electrons in its superconducting regions. Based on these results, it is
suggested that both of the observed domes form part of a single superconducting
phase. We also study the effect of the quantum critical fluctuations emerging
from the suppressed charge order on the transport properties directly above the
superconducting region, and compare our finding with reported experimental
results.
