Nodal quasi-particles and coexisting orders in striped 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 charicature of a locally 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 limit, ``d-wave like order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasi-particle spectrum, or gapless ``nodal quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.