Time-reversal symmetry breaking states at [100] surfaces of dx2-y2 superconductors

We discuss two scenarios for the low temperature splitting of the zero-energy peak in the local density of states at [100] surfaces of dx2-y2-wave superconductors, observed by Covington et al. [M. Covington, M. Aprili, E. Paraonu, L.H. Greene, F. Xu, J. Zhu, C.A. Mirkin, Phys. Rev. Lett., 79 (1997) 281 ]. Using a tight binding model in the Bogoliubov-de Gennes treatment, we find a surface phase transition towards a time-reversal symmetry breaking s + id-wave state similar to that considered by Fogelstrom et al. [M. Fogelstrom, D. Rainer, J.A. Sauls, Phys. Rev. Lett., 79 (1997) 281]. Alternatively, we show that repulsive on-site interaction between the electrons induces a surface phase transition towards a magnetic state corresponding to a local spin density wave state.