  In mean-field descriptions of nodal d-wave superconductors, generic edges
exhibit dispersionless Majorana fermion bands at zero-energy. These states give
rise to an extensive ground-state degeneracy, and are protected by
time-reversal (TR) symmetry. We argue that the infinite density of states of
these flat-bands make them inherently unstable to interactions, and show that
repulsive interactions lead to edge FM which splits the flat bands. This edge
FM offers an explanation for the observation of splitting of zero-bias peaks in
edge tunneling in High-Tc cuprate superconductors. We argue that this mechanism
for splitting is more likely than previously proposed scenarios, and describe
its experimental consequences.
