  We study the effect of inhomogeneous strain on transition-metal
dichalcogenides with a large intrinsic gap in their spectrum. It is found that,
by tuning the chemical potential, superconductivity can preserve within the
strain-induced discrete pseudo Landau levels (LLs), which introduce interesting
topological properties to these systems. As we show, the superconductivity for
integer fillings is quantum critical, and the quantum critical coupling
strength is determined by the spacing between the two LLs closest to the Fermi
level. For partial fillings, the superconducting gap is scaled linearly with
the coupling strength, and decreases rapidly when the chemical potential shifts
away from the middle of each LL. In the presence of a Zeeman field, a pair of
Majorana modes emerge simultaneously in the two valleys of strained
dichalcogenides. When valley symmetry is further destroyed, a single Majorana
mode can be expected to emerge at the edges of the strained monolayer
dichalcogenides.
