Andreev States in a d-wave superconducting quantum wires

We study the electronic spectra of wires of d-wave superconductor on a square lattice. For general wire orientations with respect to the crystal axes, we give analytical results for Andreev wire states formed at discrete energies from theninterference of two Andreev surface states. The atomic-scale behavior is reflected in the calculated local density of states, and should be observable by scanning tunneling microscopy. We discuss the relation between these Andreev states and their normal state analogues which arise simply due to the finite transverse wire dimension. For general wire orientations, the self-consistent treatment of the order parameter is found to play a crucial role. We discuss these results in the context of general questions about unconventional superconductors in restricted geometries.