Two-Dimensional Superconducting Fluctuations Associated with Charge-Density-Wave Stripes in ${\mathrm{La}}_{1.87}{\mathrm{Sr}}_{0.13}{\mathrm{Cu}}_{0.99}{\mathrm{Fe}}_{0.01}{\mathrm{O}}_4$

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

Figure 1

(a) A schematic diagram of CDW and SDW stripes and their intertwining that results in the PDW order, implying the importance of their respective modulation phases. (b) Temperature dependence of the zero-field resistivity. ${\rho }_c$ is along the $c$ axis, and ${\rho }_{ab}$ is parallel to the ${\mathrm{CuO}}_2$ planes. The green shade and dashed line denote the first and second transitions in ${\rho }_{ab}$, respectively, above the Meissner state of both ${\rho }_{ab}$ and ${\rho }_c$ ($T_c\sim 5.7\mathrm{K}$). The inset shows the ratio of ${\rho }_c$ to ${\rho }_{ab}$ as a function of temperature.

Figure 2

(a) A schematic sketch showing the RSXS experiment on LSCFO using an area detector (CCD). At the fixed CCD angle (150°), $\theta$ scans were performed. The CDW signal is aligned on the center of the CCD detector. The bottom edge area of the image is regarded as the fluorescence (Fluo.) background-dominated region. (b) RSXS patterns in the $h$ and $k$ spaces of LSCFO for various sample temperatures after subtracting the fluorescence background. The CDW patterns are centered at $q_{\mathrm{cdw}}\sim$ ($-0.233$, 0, $l$). Below $\sim 50\mathrm{K}$, the pattern tends to elongate along the $k$ direction. (c) Projected scattering profiles along the $h$ direction as a function of temperature. The solid lines are Lorentzian fits.

Figure 3

(a) Integrated intensity (up triangles) of the CDW order (left $y$ axis) and its wave vector $q_{\mathrm{cdw}}$ (down triangles, right $y$ axis) as a function of temperature. Below $\sim 50\mathrm{K}$ (denoted by the vertical dotted line), both the intensity and the $q_{\mathrm{cdw}}$ incommensurability show a different trend. The error bars represent 1 standard deviation of the fit parameters. (b) Temperature dependence of the SDW peak intensity measured by elastic neutron scattering. The SDW data was taken from Ref. [30]. The vertical dotted line at $\sim 50\mathrm{K}$ denotes the onset of the SDW order.

Figure 4

(a) FWHM (squares) of the CDW order (left $y$ axis) and the number of wavelengths (circles) for the PDW order (right $y$ axis). The number of wavelengths ($n$) is estimated by ${\xi }_{\mathrm{CDW}}/8a$, where ${\xi }_{\mathrm{CDW}}$ is calculated as 2/FWHM. Note that the FWHM and $n$ show the same trend because they are inversely proportional to each other; they are plotted with the different axis scales. The vertical gray shade denotes a characteristic temperature ($T_w$) at which the FWHM of CDW starts to change while cooling down. The vertical green shade denotes another slope change in FWHM that is close to the first anisotropic transition ($T_1$) in ${\rho }_{ab}$. Below $T_1\sim 32\mathrm{K}$, $n$ is larger than 1. (b) A schematic diagram of a ${\mathrm{CuO}}_2$ plane in LSCFO illustrating the formation of the PDW order. The PDW (fluctuation) starts to form when the domain size of CDW is over $\sim 8a$. The dashed green curves represent a situation where the PDW cannot be formed because of insufficient ${\xi }_{\mathrm{CDW}}$. The black shades denote intrinsic disorders.