Abstract:
Zero-energy Andreev bound states may be localised at a straight flat surface of a d-wave superconductor. This well-known effect strongly depends on the orientation between the boundary and the d-wave gap function. Its existence is well confirmed experimentally, for example by the measurement of zero-bias conductance peaks.
This dissertation goes further into the question of how the bound states and thus the local quasiparticle spectra are changed, if the superconductor under consideration exhibits a nontrivial boundary geometry. As a result, there is a variety of interesting and exotic effects, all of which can be explained by taking into account the reflection properties of the boundary geometry according to classical optics.
The superconductors examined in this work are for example wedge-shaped or exhibit polygonal boundaries, or they have got holes inside. However, many more nontrivial boundary geometries are also considered. Furthermore, for some of the geometries the additional influence of both an Abrikosov-vortex and an applied magnetic field on the Andreev bound states is also examined.