Theory of the striped superconductor

We define a distinct phase of matter, a pair-density wave (PDW), in which the superconducting order parameter $\varphi \left(\vec{r},{\vec{r}}^{\prime }\right)$ varies periodically as a function of position such that when averaged over the center of mass position, $\left(\vec{r}+{\vec{r}}^{\prime }\right)/2$, all components of $\varphi$ 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 ${\text{La}}_{2-x}{\text{Ba}}_x{\text{CuO}}_4$. 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.

Figure 1

Schematic model of a striped superconductor consisting of an array of superconducting regions (SC) separated by correlated insulator regions (i). The Josephson coupling between neighboring superconducting regions is $J$. If $J<0$, the system forms a striped superconducting (or PDW) state.

Figure 2

An example of a $\pi$ junction due to a rotating domain walls in a system with a $d$-wave order parameter. From left to right, the crystallographic axes rotate by $\pi /6$ across each domain wall. After three domain walls, the crystal axis has returned to itself, but the order parameter has changed sign.

Figure 3

Phase diagram for the antiferromagnetic barrier problem as a function of the pairing gap $\Delta$ (in units of the bandwidth $W=4t$) and the average density $⟨n⟩$ in the superconductors on either side of the barrier. When $\Delta$ is large or $⟨n⟩$ is close to 1 (half filling), then a negative Josephson coupling $\left(J<0\right)$ is favored.