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We investigate the potential existence of a superconducting phase in $5d$Mott insulators with an eye to hole doped Sr$_2$IrO$_4$. Using a mean-fieldmethod, a mixed singlet-triplet superconductivity, $d + p$, is observed due tothe antisymmetric exchange originating from a quasi-spin-orbit-coupling. Ourcalculation on ribbon geometry shows possible existence of the topologicallyprotected edge states, because of nodal structure of the superconducting gap.These edge modes are spin polarized and emerge as zero-energy flat bands,supporting a symmetry protected Majorana states, verified by evaluation ofwinding number and $\mathbb{Z}_2$ topological invariant. At the end, a possibleexperimental approach for observation of these edge states and determination ofthe superconducting gap symmetry are discussed based on the quasi-particleinterference (QPI) technique.

Mixed-pairing superconductivity in 5d Mott insulators with antisymmetric exchange