Superconductivity-Insensitive Order at $q\sim 1/4$ in Electron-Doped Cuprates

One of the central questions in the cuprate research is the nature of the normal state that develops into high-temperature superconductivity (HTSC). In the normal state of hole-doped cuprates, the existence of a charge density wave (CDW) is expected to shed light on the mechanism of HTSC. With evidence emerging for CDW order in the electron-doped cuprates, the CDW is thought to be a universal phenomenon in high-$T_{\mathrm{c}}$ cuprates. However, the CDW phenomena in electron-doped cuprates are quite different than those in hole-doped cuprates. Here, we study the nature of the putative CDW in an electron-doped cuprate through direct comparisons between as-grown and postannealed ${\mathrm{Nd}}_{1.86}{\mathrm{Ce}}_{0.14}{\mathrm{CuO}}_4$ (NCCO) single crystals using Cu $L_3$-edge resonant soft x-ray scattering (RSXS) and angle-resolved photoemission spectroscopy (ARPES). The RSXS result reveals that the nonsuperconducting NCCO shows the same reflections at the wave vector ($\sim 1/4$, 0, $l$) as the reported superconducting NCCO. This superconductivity-insensitive signal is quite different from the CDW reflection in hole-doped cuprates. Moreover, the ARPES result suggests that the fermiology cannot account for such wave vectors. These results call into question the universality of the CDW phenomenon in the cuprates.

Popular Summary

High-temperature superconductors are materials that conduct electricity with zero resistance at temperatures well above absolute zero. Cuprates, a type of copper-based oxide compound, exhibit this unique behavior, and one of the central focuses in cuprate research is the nature of the so-called “normal state”—the state at temperatures higher than the superconducting temperature. Researchers hope that understanding certain aspects of the normal state will shed light on the physics underlying high-temperature superconductivity. In particular, charge-density-wave (CDW) correlations—the synchronized periodic motion of charge carriers—could provide valuable insight. Given that such correlations have been seen in different types of hole-doped cuprates, it is hoped that CDW phenomena are universal to all high-$T_{\mathrm{c}}$ cuprates. Using experimental studies, we find no evidence that this is the case.

Recent evidence of CDW order in electron-doped cuprates has raised the possibility of universality; however, there are significant differences in the CDW phenomena in electron-doped cuprates and those doped with holes (the absence of an electron). We use resonant soft x-ray scattering and angle-resolved photoemission spectroscopy to explore the electron-doped cuprates, ${\mathrm{Nd}}_{2-\mathrm{x}}{\mathrm{Ce}}_{\mathrm{x}}{\mathrm{CuO}}_4$ (NCCO). We find that a putative CDW in the NCCO has characteristics that are markedly different from CDWs observed in hole-doped superconducting cuprates.

Our findings indicate that CDWs in the electron-doped cuprates are different from those in hole-doped cuprates.

Figure 1

Phase diagram of annealed and as-grown NCCO and their RSXS measurements. Phase diagram of the (a) annealed and (b) as-grown NCCO as a function of Ce doping. The red, green, and blue areas denote the long-range AFM order, SC, and the proposed CDW, respectively. Dashed lines in panel (c) denote AFM and SC boundaries after annealing as displayed in panel (a). RSXS data of the (b) annealed and (d) as-grown NCCO ($x=0.14$). These were measured at the Cu $L_3$ edge (931 eV) with $T=30\mathrm{K}$. The vertical lines indicate the peak position at $h=-0.26\pm 0.01$ reciprocal lattice units (r.l.u.).

Figure 2

Temperature dependence of the reflection at $q\sim 1/4$. (a) Temperature-dependent $h$ scans in the as-grown NCCO ($x=0.14$), measured at the Cu $L_3$ edge. The shaded areas denote the portion of the peak above the background (black line), which was taken at $T=380\mathrm{K}$. (b) Plots of peak height (upper panel) and the full width half maximum (FWHM) (lower panel) of the peaks at $h\sim -0.26$ as a function of temperature. The open and filled circles are from the annealed and as-grown NCCO, respectively. The width is about 0.085 r.l.u. over the entire temperature range. The grey shadow is a guide to the eye, and the error bars denote 1 standard deviation (s.d.) as obtained from the peak fitting.

Figure 3

Fermi surface topology in ARPES. We show Fermi surface intensity mappings for (a) annealed and (b) as-grown NCCO measured by ARPES at $T=25\mathrm{K}$ with $E_{\mathrm{ph}}=53\mathrm{eV}$. Intensities are integrated within $\pm 10\mathrm{meV}$ of $E_F$. Note that the mappings are not folded. The dashed red curves for the Fermi surface are guides to the eye. Red arrows indicate the polarization of incident x-ray (c) line cuts along the $k_y$ direction around ($\pi$, 0). Here, $k_x$ is integrated over the range [$0.95\pi$, $1.05\pi$]. The open (filled) circles denote the nesting wave-vector positions of the annealed (as-grown) NCCO. The vertical lines indicate the in-plane wave vector measured by RSXS.

Figure 4

Energy dependence of the reflection at $q\sim 1/4$. (a) The 2D map of the RSXS intensity of the as-grown NCCO at $T=30\mathrm{K}$. (b) The integrated energy profile of the as-grown $I_{\mathrm{RSXS}}$ near $h\sim -0.26$ (red circle). The integrated range is indicated by red dashed lines in Fig. 3. The profile is compared to the x-ray absorption spectroscopy (XAS) spectra using fluorescence yield (FY). We show the $h$ scans of (c) annealed and (d) as-grown NCCO ($T=30\mathrm{K}$) at different photon energies: Cu $L_3$ edge, pre-edge, and postedge are 931 eV, 922 eV, and 936 eV, respectively. Data are vertically shifted without scaling for better visibility. The red vertical bars indicate the $h$ positions of the features.