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Motivated by the recent observations of nodeless superconductivity in themonolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$substrates, we study the two-dimensional superconducting (SC) phases describedby the two-dimensional $t$-$J$ model in proximity to an antiferromagnetic (AF)insulator. We found that (i) the nodal d-wave SC state can be driven via acontinuous transition into a nodeless d-wave pairing state by the proximityinduced AF field. (ii) The energetically favorable pairing states in the strongfield regime have extended s-wave symmetry and can be nodal or nodeless. (iii)Between the pure d-wave and s-wave paired phases, there emerge twotopologically distinct SC phases with ($s+$i$d$) symmetry, i.e., the weak andstrong pairing phases, and the weak pairing phase is found to be a $Z_{2}$topological superconductor protected by valley symmetry, exhibiting robustgapless non-chiral edge modes. These findings strongly suggest that thehigh-$T_{c}$ superconductors in proximity to antiferromagnets can realize fullygapped symmetry protected topological SC.

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets