Direct observation of bulk charge modulations in optimally doped ${\mathrm{Bi}}_{1.5}{\mathrm{Pb}}_{0.6}{\mathrm{Sr}}_{1.54}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

Bulk charge density modulations, recently observed in high critical-temperature $\left(T_{\mathrm{c}}\right)$ cuprate superconductors, coexist with the so-called pseudogap and compete with superconductivity. However, its direct observation has been limited to a narrow doping region in the underdoped regime. Using energy-resolved resonant x-ray scattering we have found evidence for such bulk charge modulations, or soft collective charge modes (soft CCMs), in optimally doped ${\mathrm{Bi}}_{1.5}{\mathrm{Pb}}_{0.6}{\mathrm{Sr}}_{1.54}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Pb-Bi2212) around the summit of the superconducting dome with momentum transfer $q_{\parallel }\sim 0.28$ reciprocal lattice units (r.l.u.) along the Cu-O bond direction. The signal is stronger at $T\simeq T_{\mathrm{c}}$ than at lower temperatures, thereby confirming a competition between soft CCMs and superconductivity. These results demonstrate that soft CCMs are not constrained to the underdoped regime, suggesting that soft CCMs appear across a large part of the phase diagram of cuprates and are intimately entangled with high-$T_{\mathrm{c}}$ superconductivity.

Figure 1

Resonant soft x-ray scattering from optimally doped Bi2212. (a) Scattering geometry with the $c$ and either $a$ or $b$ axes in the scattering plane. The incident photon polarization can be parallel ($\pi )$ or perpendicular ($\sigma )$ to the scattering plane. (b) RIXS spectrum at $q_{\parallel }\simeq 0.25$ r.l.u. Quasielastic peak, phonon excitations ($\sim$$-0.07$ eV), dispersing paramagnons ($<$$-0.35$ eV), and the $d$-$d$ excitations around $-2$ eV are indicated. (c) and (d) Low-energy RIXS intensity map taken at $T\sim 50$ K along the Cu-O bond direction with $\pi$ and $\sigma$ polarizations, respectively. The temperature dependent measurements, shown in the next figures, were carried out with $\sigma$ polarization in the momentum transfer region indicated by the box.

Figure 2

Temperature dependence of the RIXS spectra across $T_{\mathrm{c}}$. (a) and (b) RIXS intensity map taken with $\sigma$ polarization at $T\sim 20$ K ($\sim$$T_{\mathrm{c}})$ and 96 K ($\ll$$T_{\mathrm{c}})$, respectively. (c) Color map for 96–20 K showing a strong temperature dependence at $q_{\parallel }\sim 0.28$ rlu.

Figure 3

A signature of the soft CCMs at $q_{\parallel }\sim 0.28$ r.l.u. (a) RIXS spectra at 96 K (red) and 20 K (blue) at selected $q_{\parallel }$. The differences between the two temperatures are highlighted by the green shading. (b) Temperature dependence of the intensity at $0\pm 0.1$ eV for the quasielastic signal and (c) $-0.4\pm 0.1$ eV for the multimagnon signal, respectively. The 20 and 96 K intensities are from the experiment No. 1 and the 50 K intensities are from the experiment No. 2. The differences between 96 and 20 K are also plotted (open green triangles).