Long-range two-dimensional superstructure in the superconducting electron-doped cuprate ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_4$

Utilizing single-crystal synchrotron x-ray scattering, we observe distorted ${\text{CuO}}_2$ planes in the electron-doped superconductor ${\mathrm{Pr}}_{1-x}{\mathrm{LaCe}}_x{\mathrm{CuO}}_{4+\delta }, x$ = 0.12. Resolution-limited rods of scattering are indicative of a long-range two-dimensional $2\sqrt{2}\times 2\sqrt{2}$ superstructure in the $a-b$ plane, adhering to planar space-group symmetry $p4gm$, which is subject to stacking disorder perpendicular to the planes. This superstructure is present only in annealed, superconducting samples, but not in the as-grown, nonsuperconducting samples. These long-range distortions of the ${\mathrm{CuO}}_2$ planes, which are generally considered to be detrimental to superconductivity, have avoided detection to date due to the challenges of observing and interpreting subtle diffuse-scattering features.

Figure 1

Two-dimensional single-crystal x-ray diffuse scattering scan from the $L_c=3$ reciprocal-space plane of the r-SC sample of PLCCO. Symbols are used to indicate visible signals at superlattice peak positions relative to the reciprocal lattice of the parent cuprate: circles for (1/2,1/2)-type peaks, ellipses for (1/2,0)-type peaks, and squares for (1/4,1/4)-type peaks. The concentrated intensity surrounding each of the intense Bragg reflections of the parent cuprate is thermal-diffuse scattering, and it is nominally identical among all of the samples studied. Superlattice intensities were only observed in the SC samples.

Figure 2

(a) Scans along $(8.25,0.25,L_c)$ in the o-NSC (red) and r2-SC (blue) PLCCO samples. A modulated needle of diffuse scattering is apparent below a series of sharp sesquioxide impurity peaks. (b) Scans along $(8.0+H,0.5-H,0.05)$ in the same two samples. (c) Relative intensity trend of the diffuse needles located at positions $(H=n+1/2,K=1/2)$ for integers $n$ in the range 0 to 12, where each closed black circle represents the amplitude of a Gaussian fit to an $H$ scan through the corresponding needle at $L_c=4.9$, and where blue diamonds and green squares indicate fitted values based on respective planar-distortion models A and B. The perpendicular scans in (a) and (b) intersect at their respective centers, both having peaks at $(8.25,0.25,0)$. The broad peak below the needle peak in (b) is thermal-diffuse scattering (TDS) associated with the parent $(8,0,0)$ Bragg peak. This TDS scattering was measured along lines offset from the diffuse needles and then subtracted from the needles to produce panel (a).

Figure 3

Blue indicates scans along the diffuse needles located at (a) $(6.25,5.75,L_c)$, (b) $(6.75,6.25,L_c)$, (c) $(6.25,6.25,L_c)$, and (d) $(6.75,5.75,L_c)$ over the range between $L_c=\pm 7$ in the r2-SC sample of PLCCO. Green indicates two TDS scans separated from the corresponding diffuse needle $\left|\mathrm{\Delta }H\right|=\left|\mathrm{\Delta }K\right|=0.03$ r.l.u., one being slightly closer to the nearest parent Bragg peak and the other slightly farther away. Red indicates TDS-corrected diffuse-needle data, which were obtained by subtracting the average of the two green scans from the corresponding blue scan.

Figure 4

Illustrations of superstructural planar distortion models (a) A and (b) B of the ${\mathrm{CuO}}_2$ sheets of PLCCO, both of which have planar symmetry $p4gm$. The distortion amplitudes have been exaggerated for visual clarity.

Figure 5

Illustration of the symmetry-distinct supercell-origin options in the nearest-neighbor (left) and next-nearest-neighbor (right) sheets of PLCCO. The dashed and solid lines delineate the parent cuprate cell and the $2\sqrt{2}\times 2\sqrt{2}$ supercell, respectively, while blue squares represent individual ${\mathrm{CuO}}_2$ units. The four-arm star symbol at the center of each sheet indicates the location of the supercell origin in the primary ($n=0$) ${\mathrm{CuO}}_2$ sheet, while small circles indicate the eight possible supercell-origin locations in a neighboring sheet. Observe that the supercell origin in the nearest-neighbor sheet cannot lie directly on top of the origin in the primary sheet due to the body-centered relationship between adjacent sheets. The Greek symbols in the legend at the top of the figure represent the probabilities of finding the supercell origin at the corresponding sites. Thus, the collective probability that the origin will lie in one of the speckled-circle sites in the nearest-neighbor sheet is $\alpha$. Because the placement probabilities in a given sheet must add up to 1, we have $\alpha +{\alpha }^{\prime }=1$ in the nearest-neighbor sheet and $\beta +\delta +\gamma +\epsilon =1$ in the next-nearest-neighbor sheet. A strictly random distribution would have $\alpha /4={\alpha }^{\prime }/4=\beta /4=\delta /2=\gamma =\epsilon =1/8$, so that all origin sites are equally probable.