Abstract
The spatial variations of the order parameter and the local density of states on the corner of s-wave or ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductors, as well as in superconductor--insulator--normal metal interfaces, are calculated self-consistently by exact diagonalization of the Bogoliubov--de Gennes Hamiltonian within the two-dimensional extended Hubbard model. Due to the suppression of the dominant d-wave order parameter, the extended s-wave order parameter is induced near the surface, which alternates its sign for the topmost sites at adjacent edges of the lattice and decays to zero in the bulk. The presence of surface roughness results in the appearance of a zero-bias conduction peak near the corner surface which is lacking from the predictions of the quasiclassical theory.
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