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In mean-field descriptions of nodal d-wave superconductors, generic edgesexhibit dispersionless Majorana fermion bands at zero-energy. These states giverise to an extensive ground-state degeneracy, and are protected bytime-reversal (TR) symmetry. We argue that the infinite density of states ofthese flat-bands make them inherently unstable to interactions, and show thatrepulsive interactions lead to edge FM which splits the flat bands. This edgeFM offers an explanation for the observation of splitting of zero-bias peaks inedge tunneling in High-Tc cuprate superconductors. We argue that this mechanismfor splitting is more likely than previously proposed scenarios, and describeits experimental consequences.

Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates