Theory of the striped superconductor

We define a distinct phase of matter, a pair-density wave (PDW), in which the superconducting order parameter phi(r,r(')) varies periodically as a function of position such that when averaged over the center of mass position, (r+r('))/2, all components of phi vanish identically. Specifically, we study the simplest unidirectional PDW, the striped superconductor, which we argue may be at the heart of a number of spectacular experimental anomalies that have been observed in the failed high-temperature superconductor La2-xBaxCuO4. We present a solvable microscopic model with strong electron-electron interactions which supports a PDW ground state. We also discuss, at the level of Landau theory, the nature of the coupling between the PDW and other order parameters and the origins and some consequences of the unusual sensitivity of this state to quenched disorder.