  We theoretically study potential unconventional superconductivity in doped
AB-type IV-VI semi-conductors, based on a minimal effective model with
interaction up to the next-nearest neighbors. According to the experimental
implications, we focus on the spin-triplet channels and obtain the
superconducting phase diagram with respect to the anisotropy of the Fermi
surfaces and the interaction strength. Abundant nodal and nodeless states with
different symmetry breaking appear in the phase diagram, and all the states are
time reversal invariant and topologically nontrivial. Specifically, the various
nodal superconducting ground states, dubbed as the topological Dirac
superconductors, are featured by Dirac nodes in the bulk and Majorana arcs on
the surface; among the full-gap states, there exist a mirror-symmetry-protected
second-order topological superconductor state favoring helical Majorana hinge
cones, and different first-order topological superconductor states supporting 4
surface Majorana cones. The experimental verification of the different kinds of
superconducting ground states is also discussed.
