Signatures of pair-density wave order in phase-sensitive measurements of La$_{2-x}$Ba$_x$CuO$_4$-Nb Josephson junctions and SQUIDs

The interplay of charge order, spin order, and superconductivity in La$_{2-x}$Ba$_x$CuO$_4$ creates a complex physical system that hosts several interesting phases, such as two-dimensional superconductivity within the CuO$_2$ planes and the ordered pair-density wave state in which charge ordering is intertwined with superconductivity. Using Josephson interferometry techniques, we measure the current-phase relation of junctions and SQUIDs incorporating this material and observe a significant sin($2phi$)-component indicative of closely-spaced alternations of the sign of the Josephson coupling predicted by the pair-density wave model. We find that the ratio of the sin(2$phi$)-component to the conventional sin($phi$)-component to be largest near x=1/8 doping, where the pair-density wave state is believed to be the strongest, and that it increases with increasing temperature as the Josephson coupling in the junction weakens.