Nodal quasiparticles in stripe ordered superconductors

We study the properties of a quasi-one-dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple caricature of a striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi-liquid normal state. Even in this lit-nit, d-wave-like order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasiparticle spectrum, or gapless nodal quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.