Density of states width-parity effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e., a sample of infinite length but finite width N. For open boundary conditions and half-filling, the DOS at zero energy is found to be zero if N is even and nonzero if N is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd N remain.