Zero-energy Andreev surface bound states in the lattice model

The conditions for zero-energy Andreev surface bound states to exist are found for the lattice model of a d-wave superconductor with arbitrary surface orientation. Both nearest-neighbors and next-nearest-neighbors models are considered. It is shown that the results are very sensitive to the surface orientation. In particular, for a half-filled (hl0)-surface, zero-energy Andreev surface states only appear under the condition that h and l are odd simultaneously.