| We have studied the effects of inhomogeneities like surfaces, interfaces and disorder on the properties of s-wave and d-wave superconductors. The description of such inhomogeneous scenarios is very important, as they have a big influence on experimental observations. Tunneling experiments on the surface of superconductors will have a direct look into these peculiar surface states, like the zero bias conductance peak and the Andreev bound states.;Using the tight-binding Extended Hubbard Hamiltonian, we numerically solve the discretized Bogoliubov-de Gennes equations applied to various inhomogeneous problems. We use simplifications due to the symmetries of surfaces, to solve problems like superconductivity near a surface, the giant proximity effect and the formation of Andreev bound states. Full two-dimensional calculations are employed to describe rough surfaces, finite size systems and the localization of the Andreev bound states in finite size samples.;We find that the order parameter near surfaces exhibits Friedel-like oscillations on the order of the Fermi wavelength, and that interference effects occur in finite size systems. Major differences between the properties of d-wave superconductors near the (100) surface as compared to the (110) surface are uncovered. Zero energy bound states are present not only at the (110) surface of a d-wave superconductor, but also in a normal metal layer sitting on top of a d-wave superconductor. We demonstrate that rough surfaces of d-wave superconductors will acquire zero energy bound states at any surface orientation. We observe that Andreev bound states form in a normal metal when it is in proximity to a superconductor, and we show that in the case of finite size systems these states are localized in different locations depending on their energy.;... |
