  We solve the Bogoliubov-de Gennes equations self-consistently for d-wave
superconductors with [110] surfaces. We find spontaneous breaking of
time-reversal symmetry (TRS) caused by the spontaneous occurrence of a complex
order parameter with an extended s-wave symmetry along the [110] surfaces. In
the TRS-breaking phase, the d-wave order parameter itself becomes complex. We
also show that vortex-antivortex pairs can appear along the [110] surfaces of
nanoribbons. These pairs are detectable with surface sensitive probes.
