Different scenarios for the low-temperature splitting of the zero-energy pe
ak in the local density of states at (1 1 0) surfaces of d(x2 - y2) -wave s
uperconductors are compared with each other. For a pure dx(2) - y(2)-wave s
uperconductor surface bound states generate a large density of states at th
e Fermi level. This causes local instabilities which occur either towards a
time reversal symmetry breaking superconducting state (s + id-type) or a m
agnetic slate with staggered magnetic moments. We show that both types of a
local symmetry breaking would lead to similar splittings of the zero-energ
y peak. (C) 2000 Elsevier Science B.V. All rights reserved.