Time-reversal symmetry breaking stares at [110] surfaces of d(x2-y2) superconductors

We discuss two scenarios for the low temperature splitting of the zero-ener gy peak in the local density of states at [110] surfaces of d(x2-y2)-wave s uperconductors, observed by Covington et al. [M. Covington, M. Aprili, E. P araonu, 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 breakin g s + id-wave state similar to that considered by Fogelstrom et al. [M. Fog elstrom, D. Rainer, J.A. Sauls, Phys. Rev. Lett., 79 (1997) 281]. Alternati vely: we show that repulsive on-site interaction between the electrons indu ces a surface phase transition towards a magnetic state corresponding to a. local spin density wave state. (C) 1999 Elsevier Science B.V. All rights r eserved.