Evidence for Weakly Correlated Oxygen Holes in the Highest-$T_c$ Cuprate Superconductor ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$

We study the electronic structure of ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ (Hg1223; $T_c=134\mathrm{K}$) using photoemission spectroscopy (PES) and $x$-ray absorption spectroscopy (XAS). Resonant valence band PES across the O $K$ edge and Cu $L$ edge identifies correlation satellites originating in O $2p$ and Cu $3d$ two-hole final states, respectively. Analyses using the experimental O $2p$ and Cu $3d$ partial density of states show quantitatively different on-site Coulomb energy for the Cu site ($U_{dd}=6.5\pm 0.5\mathrm{eV}$) and O site ($U_{pp}=1.0\pm 0.5\mathrm{eV}$). ${\mathrm{Cu}}_2{\mathrm{O}}_7$-cluster calculations with nonlocal screening explain the Cu $2p$ core level PES and Cu $L$-edge XAS spectra, confirm the $U_{dd}$ and $U_{pp}$ values, and provide evidence for the Zhang-Rice singlet state in Hg1223. In contrast to other hole-doped cuprates and $3d$-transition metal oxides, the present results indicate weakly correlated oxygen holes in Hg1223.

Figure 1

Photon energy dependent valence band PES of ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ (Hg1223) measured using $h\nu =21.2$, 524.4, 926.3, and 1200 eV. The spectra are normalized at 5 eV BE. The experimental Cu $3d$ PDOS, obtained as a difference spectrum between $h\nu =1200\mathrm{eV}$ and $h\nu =21.2\mathrm{eV}$ spectra, is also plotted. The inset shows the Fermi step for Hg1223 and gold reference along with a fit to the Fermi-Dirac distribution convoluted with a Gaussian function. The He $I$ ($h\nu =21.2\mathrm{eV}$) spectrum is a laboratory measurement at $T=120\mathrm{K}$ and all other spectra are measured at $T=20\mathrm{K}$ using synchrotron radiation.

Figure 2

(a) The Cu $L_3$-edge ($2p\text{−}3d$) XAS of Hg1223 measured at $T=20\mathrm{K}$. The labels $a–j$ indicate $h\nu$ used for measuring Cu $2p\text{−}3d$ resonant valence band PES of Hg1223 shown in panel (b). (b) Resonant PES showing the sharp peak at 12.6 eV BE obtained with $h\nu =931.2\mathrm{eV}$ [main peak in XAS; label $\mathbf{d}$ in panel (a)] is the $3d^8$ giant resonance feature. The thin black vertical line shows that the $3d^8$ resonance peak stays fixed at 12.8 eV BE up to $h\nu =931.2\mathrm{eV}$ and evolves into the Cu $L_3\mathrm{VV}$ Auger satellite for higher $h\nu$. (c) The O $K$ edge ($1s\text{−}2p$) XAS of Hg1223 measured at $T=20\mathrm{K}$. The labels ${\mathbf{a}}^{\prime }-{\mathbf{g}}^{\prime }$ mark the photon energies used for measuring the O $1s\text{−}2p$ resonant valence band PES shown in panel d. (d) The $2p^4$ resonance satellite arising due to on-site $U_{pp}$ correlations gets enhanced but stays fixed up to a photon energy of 527.6 eV [label ${\mathbf{c}}^{\prime }$ in panel (a)] and evolves into the O $K\mathrm{VV}$ Auger satellite for higher photon energies. All resonant PES spectra are normalized for incident photon flux and number of scans.

Figure 3

(a) The Cu $2p\text{−}3d$ resonant PES spectra [labeled $\mathbf{a}$ and $\mathbf{b}$, from Fig. 2] measured at $T=20\mathrm{K}$ (normalized at the O $2s$ feature at $\sim 24\mathrm{eV}$ BE) showing the resonantly enhanced correlation satellite at 12.8 eV compared with the self-convolution of Cu $3d$ PDOS shown in Fig. 1. The energy separation between the main peaks gives $U_{dd}=6.5\pm 0.5\mathrm{eV}$. (b) The O $1s\text{−}2p$ resonant PES spectra [labeled ${\mathbf{a}}^{\prime }-{\mathbf{c}}^{\prime }$, from Fig. 2] measured at $T=20\mathrm{K}$ (normalized at the O $2s$ feature at $\sim 24\mathrm{eV}$ BE) showing the resonantly enhanced correlation satellite at 11.6 eV BE compared with the self-convoluted O $2p$ PDOS. The energy separation between the main peaks gives $U_{pp}=1.0\pm 0.5\mathrm{eV}$.

Figure 4

(a) The Cu $2p_{3/2}$ PES of Hg1223 measured at $T=20\mathrm{K}$ compared with a ${\mathrm{Cu}}_2{\mathrm{O}}_7$ cluster calculation with nonlocal screening. (b) The Cu $L_3$-edge XAS of Hg1223 measured at $T=20\mathrm{K}$ compared with a ${\mathrm{Cu}}_2{\mathrm{O}}_7$ cluster calculation with nonlocal screening.