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 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 half-filled (hl0)-surface zero-energy Andreev surface states only appear under the condition that h and l are odd simultaneously. Significant feature of high temperature superconductors (HTS) are zeroenergy Andreev surface bound states. The zero-energy states (ZES) form on surfaces of a d-wave superconductor with orientations different from the (100), due to the sign change of the order parameter. In high-temperature superconductors, such states manifest themselves as the zero-bias conductance peak in tunneling spectroscopy in the ab-plane [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], the anomalous temperature behavior of the Josephson critical current [27, 28, 29, 30] and the upturn in the temperature dependence of the magnetic penetration depth [31, 32, 33]. At the same time the problem of ZES at the surface with arbitrary orientation is still not clear.