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The presence of a small concentration of in-plane Fe dopants inLa$_{1.87}$Sr$_{0.13}$Cu$_{0.99}$Fe$_{0.01}$O$_4$ is known to enhancestripe-like spin and charge density wave (SDW and CDW) order, and suppress thesuperconducting $T_c$. Here, we show that it also induces highlytwo-dimensional (2D) superconducting correlations that have been argued to besignatures of a new form of superconducting order, so-called pair-density-wave(PDW) order. In addition, using the resonant soft x-ray scattering, we findthat the 2D superconducting fluctuation is strongly associated with the CDWstripe. In particular, the PDW signature first appears when the correlationlength of the CDW stripe grows over eight times the lattice unit ($\sim$ 8$a$).These results provide critical conditions for the formation of PDW order.

Two-dimensional superconducting fluctuations associated with charge density wave stripes in La$_{1.87}$Sr$_{0.13}$Cu$_{0.99}$Fe$_{0.01}$O$_4$