Evolving Picture of Striped Superconductivity in La$_{2-x}$Ba$_x$CuO$_4$

We have previously presented experimental evidence for two-dimensional superconductivity in La$_{1.875}$Ba$_{0.125}$CuO$_4$ coexisting with charge and spin stripe order for $T < 40$ K. A pair-density-wave (PDW) state has been proposed to explain the dynamical layer decoupling; however, recent photoemission measurements indicate that a $d$-wave gap develops on the nodal arc in the same temperature range. We show that our various experimental results are consistent with the onset of PDW correlations together with the charge-stripe order at 53 K, followed by the development of uniform $d$-wave superconductivity. We can rule out layer decoupling due to a charge-density-wave gap.