Emergence of d±ip -wave superconducting state at the edge of d -wave superconductors mediated by ferromagnetic fluctuations driven by Andreev bound states

We propose a mechanism of spin-triplet superconductivity at the edge of $d$-wave superconductors. Recent theoretical research on $d$-wave superconductors predicted that strong ferromagnetic (FM) fluctuations are induced by a high density of states due to edge Andreev bound states (ABSs). Here, we construct a linearized gap equation for the edge-induced superconductivity and perform a numerical study based on a large cluster Hubbard model with a bulk $d$-wave superconducting (SC) gap. We find that ABS-induced strong FM fluctuations mediate the $d\ifmmode\pm\else\textpm\fi{}ip$-wave SC state, in which the time-reversal symmetry is broken. The edge-induced $p$-wave transition temperature ${T}_cp$ is slightly lower than the bulk $d$-wave one ${T}_cd$, and a Majorana bound state may be created at the end point of the edge.