Instabilities at [110] surfaces of d(x2-y2) superconductors

We compare different possible origins for the low-temperature splitting of the zero-energy peak in the local density of states at (110) surfaces of d( x2-y2)-waw superconductors. Using a tight-binding model with interactions i n the Bogolybov-de Gennes treatment, we discuss the instability of the, sup erconductor against a current-carrying locally time-reversal symmetry-break ing phase (s + id-wave) and, alternatively, a spin density wave-like state. The former (latter) is more likely to occur in a regime corresponding to t he overdoped (underdoped) situation of high-temperture superconductors.