Local density of states on rough surfaces of dx(2)-y(2)-wave superconductors

The spatial variations of the local density of states (LDOS) on the surface of d(x2-y2)-wave superconductors are calculated using an extended Hubbard model. Our model has the ability to treat the surface geometry with atomic-scale roughness, and gives realistic results beyond those based on the quasiclassical theory. The spatial variation of the LDOS is obtained for various types of surface geometries using a self-consistently determined pair potential. As surface bound states are peculiar to d-wave superconductors, we pay attention to the appearance of zero-energy states (ZES's). For a flat surface, the formation of a ZES on a [110] surface and the lack of one on a [100] surface is obtained, which is consistent with the results of the quasiclassical theory. However, the LDOS shows abundant spatial dependence when the surfaces have roughness. The appearance of a ZES on nominal [100] surfaces and its disappearance on nominal [110] surfaces are obtained depending on geometry. The calculations explain the origin of various spectra observed by tunneling spectroscopy on high-T-c superconductors.