Pair-density wave signature observed by x-ray scattering in La-based high-T_(rm c) cuprates

Suggestive, but indirect evidence of the existence of pair-density wave (PDW) order in several high-$T_{\rm c}$ cuprates has been reported. As this constitutes a new quantum phase of matter, it is important to {\it establish} its existence at least somewhere in the phase diagram. However, a direct correspondence between experiment and theory has remained elusive. Here, we report the observation of a theoretically predicted PDW {\it bulk} signature in two La-based cuprates, Sr-doped La$_{1.875}$Ba$_{0.125}$CuO$_4$ and Fe-doped La$_{1.87}$Sr$_{0.13}$CuO$_4$, through a comprehensive study that incorporates zero-magnetic field x-ray scattering, neutron scattering, and transport measurements. Specifically, we observe the emergence of so-called "1Q" order, which is to say subharmonic order associated with the charge-density wave (CDW) stripes, in a range of temperatures in which independent evidence suggests the co-existence of PDW long-range order and fluctuating uniform superconducting order. The subharmonic order is most pronounced around a half-integer $l$-vector, where the CDW diffraction peak is also strongest. This is consistent with the theoretical proposal that the cancellation of the Josephson coupling ("layer-decoupling"), is a signature of PDW order and that it is commensurately locked to the density wave stripes that are known to alternate orientation between adjacent layers. Even if the PDW is not the "mother of all state", it is at least a close relative -- possibly a second cousin.