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 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 ferromagnetism which splits the flat bands. This edge ferromagnetism offers an explanation for the observation of the splitting of zero-bias peaks in edge tunneling in high-$T_c$ cuprate superconductors. We argue that this mechanism for splitting is more likely than previously proposed scenarios and describe its experimental consequences.

• Received 1 April 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.117002