Grains and wires of d-wave superconductors

We investigate Andreev states in grains of d-wave superconductors and compare them with a previous analysis of d-wave quantum wires. For perfect nesting a zero-energy Andreev bound state exists for geometries containing an odd number of (110)-layers. Away from perfect nesting the Andreev resonance broadens and its resonance frequency becomes finite for small grains. With increasing system size the resonance frequency approaches zero at least when we assume a constant order parameter throughout the grain. This is contrary to (110)-wires, where the Andreev state occurs at zero energy for all wire widths. Multiple reflections from surfaces with different orientations give rise to interesting interference effects and modify the Andreev states near corners.