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We propose a mechanism of spin-triplet superconductivity at the edge of$d$-wave superconductors. Recent theoretical research in $d$-wavesuperconductors predicted that strong ferromagnetic (FM) fluctuations areinduced by large density of states due to edge Andreev bound states (ABS).Here, we construct the linearized gap equation for the edge-inducedsuperconductivity, and perform a numerical study based on a large clusterHubbard model with bulk $d$-wave superconducting (SC) gap. We find thatABS-induced strong FM fluctuations mediate the $d \pm ip$-wave SC state, inwhich the time-reversal symmetry is broken. The edge-induced $p$-wavetransition temperature $T_{cp}$ is slightly lower than the bulk $d$-wave one$T_{cd}$, and the Majorana bound state may be created at the endpoint of theedge.

physical review. b./physical review. b

Emergence of $d \pm ip$-wave superconducting state at the edge of  $d$-wave superconductors mediated by Andreev-bound-state-driven ferromagnetic  fluctuations