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±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.

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