Spatial dependencies of the pair potential and the local density of states near the surfaces of
dx2−y2-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction
J is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-
Tc superconductors.
As the surface Andreev bound state (ABS) forms at the open (1,1) edge of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, the local density of states increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study the large-cluster Hubbard model with an open (1,1) edge in the presence of a bulk
d-wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk
d-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.
We study interacting molecules on the surface of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor. We show that the interplay between the molecules' excitation spectrum and quantum interference of the scattered host electrons leads to a series of characteristic signatures and intriguing quantum effects in the superconductor's local density of states. We demonstrate that these effects give insight into both the nature of the superconducting pairing correlations and the intermolecular interactions.