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

TL;DR

This paper explores how proximity to antiferromagnetic insulators can induce topological and nodeless superconducting phases in two-dimensional d-wave superconductors, revealing new topological states and phase transitions.

Contribution

It demonstrates the emergence of topologically distinct superconducting phases, including a $Z_{2}$ topological superconductor, in a 2D $t$-$J$ model near antiferromagnets, with potential relevance to high-$T_c$ materials.

Findings

Nodal d-wave state transitions to nodeless d-wave via AF field.

Extended s-wave pairing states can be nodal or nodeless.

Existence of $Z_{2}$ topological superconductor with gapless edge modes.

Abstract

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ substrates, we study the two-dimensional superconducting (SC) phases described by 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 a continuous transition into a nodeless d-wave pairing state by the proximity induced AF field. (ii) The energetically favorable pairing states in the strong field 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 two topologically distinct SC phases with ($s+$i$d$) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a $Z_{2}$ topological superconductor protected by valley symmetry, exhibiting robust gapless non-chiral edge modes. These findings strongly suggest that the high-$T_{c}$ superconductors in proximity to antiferromagnets can realize fully gapped symmetry protected topological SC.