Resonant inelastic x-ray scattering study of intraband charge excitations in hole-doped high-$T_c$ cuprates

We have performed resonant inelastic x-ray scattering (RIXS) near the Cu-$K$ edge on cuprate superconductors La${}_{2-x}$Sr${}_x$CuO${}_4$, La${}_{2-x}$Ba${}_x$CuO${}_4$, La${}_{2-x}$Sr${}_x$Cu${}_{1-y}$Fe${}_y$O${}_4$, and Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$, covering underdoped to heavily overdoped regimes and focusing on charge excitations inside the charge-transfer gap. RIXS measurements of the 214 systems with $E_i=8.993$ keV have revealed that the RIXS intensity at 1-eV energy transfer has a minimum at $(0,0)$ and maxima at $(\pm 0.4\pi ,0)$ and $(0,\pm 0.4\pi )$ for all doping points regardless of the stripe-ordered state, suggesting that the corresponding structure is not directly related to stripe order. Measurements with $E_i=9.003$ keV on metallic La${}_{1.7}$Sr${}_{0.3}$CuO${}_4$ and Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$ exhibit a dispersive intraband excitation below 4 eV, similar to that observed in the electron-doped Nd${}_{1.85}$Ce${}_{0.15}$CuO${}_4$. This is the first observation of a dispersive intraband excitation in a hole-doped system, evidencing that both electron- and hole-doped systems have a similar dynamical charge correlation function.

Figure 1

Fluorescence spectra for (a) La${}_2$CuO${}_4$ (dashed line) and La${}_{1.7}$Sr${}_{0.3}$CuO${}_4$ (solid line) as a representative spectra of the LSCO system and (b) Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$. For each material, fluorescence was measured with two conditions: ${\epsilon }_i\parallel c$ and ${\epsilon }_i\parallel a$. For the LSCO system, RIXS measurements were done at $E_i=8.993$ and $9.003$ keV, while those for Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$ were done at $E_i=9.003$ keV.

Figure 2

Panels (a), (b), and (c) show RIXS spectra at $(0,0)$, $(\pi /2,0)$, and $(\pi ,0)$, respectively, for the Ba0.08, Sr0.15, and Sr0.30 samples, measured with $E_i=8.993$ keV. The RIXS intensity below 3 eV increases monotonically with doping. (d) Scattering geometry of the present study. (e) The RIXS intensity profiles at an energy transfer of 1 eV along the $H$ direction for the three samples. (f) Hole-concentration dependence of the RIXS intensity at 1 eV at $(0,0)$, $(\pi /2,0)$, and $(\pi ,0)$.

Figure 3

Contour plots of RIXS intensity at 1 eV for (a) La${}_{1.92}$Ba${}_{0.08}$CuO${}_4$, (b) La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$, (c) La${}_{1.85}$Sr${}_{0.15}$CuO${}_4$, (d) La${}_{1.70}$Sr${}_{0.30}$CuO${}_4$, and (e) La${}_{1.85}$Sr${}_{0.15}$Cu${}_{0.99}$Fe${}_{0.01}$O${}_4$. The intensity in each figure is corrected by an absorption factor $1+\tan \left(\theta \right)$ and normalized to the maximum intensity in each plot.

Figure 4

Comparison between RIXS spectra of La${}_{1.70}$Sr${}_{0.30}$CuO${}_4$ measured with $E_i=8.993$ keV (circles) and $9.003$ keV (squares) at (a) $(0,0)$, (b) $(\pi ,0)$, and (c) $(\pi ,\pi )$. Panel (d) compares $H$-scan profiles of RIXS intensity at 1 eV. In all figures, the data with $E_i=9.003$ keV are multiplied by 3 or 5, for clarity.

Figure 5

$\mathbf{q}$ dependence of the RIXS spectra of La${}_{1.70}$Sr${}_{0.30}$CuO${}_4$ measured with $E_i=8.993$ keV along (a) the $(0,0)$ to $(\pi ,0)$ direction and (b) the $(0,0)$ to $(\pi ,\pi )$ direction. Each spectrum is shifted by 1 cps for clarity. Dashed and solid lines indicate fits to the elastic component, the molecular orbital excitation centered at 8 eV, and their sum, respectively. Panels (c) and (d) are analogous plots for Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$. Data at $(0,0)$ and $(\pi ,\pi )$ are missing due to contamination by large elastic components

Figure 6

RIXS intensity after the subtraction of the elastic and molecular orbital components for La${}_{1.70}$Sr${}_{0.30}$CuO${}_4$ (solid circles) and Bi${}_{1.76}$Pb${}_{0.35}$Sr${}_{1.89}$CuO${}_{6+\delta }$ (open circles). (a) $\mathbf{q}$ dependence along the $(0,0)$ to $(\pi ,0)$ direction. (b) $\mathbf{q}$ dependence along the $(0,0)$ to $(\pi ,\pi )$ direction. Arrows indicate the center of mass of the remnant intensity of LSCO with $x=0.30$ determined by fitting to a Gaussian function.

Figure 7

A $\mathbf{q}$-$E$ contour plot of the RIXS intensity after the subtraction of the elastic and molecular orbital components for La${}_{1.70}$Sr${}_{0.30}$CuO${}_4$. Circles indicate the positions of the center of mass for LSCO with $x=0.30$ shown by arrows in Fig. 6, while squares indicate those for NCCO adopted from Ref. 15.