Probing inter- and intrachain Zhang-Rice excitons in ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and determining their binding energy

Cuprate materials, such as those hosting high-temperature superconductivity, represent a famous class of materials where the correlations between the strongly entangled charges and spins produce complex phase diagrams. Several years ago, the Zhang-Rice singlet was proposed as a natural quasiparticle in hole-doped cuprates. The occurrence and binding energy of this quasiparticle, consisting of a pair of bound holes with antiparallel spins on the same ${\mathrm{CuO}}_4$ plaquette, depends on the local electronic interactions, which are fundamental quantities for understanding the physics of the cuprates. Here, we employ state-of-the-art resonant inelastic x-ray scattering (RIXS) to probe the correlated physics of the ${\mathrm{CuO}}_4$ plaquettes in the quasi-one-dimensional chain cuprate ${\mathrm{Li}}_2{\mathrm{CuO}}_2$. By tuning the incoming photon energy to the O $K$ edge, we populate bound states related to the Zhang-Rice quasiparticles in the RIXS process. Both intra- and interchain Zhang-Rice singlets are observed and their occurrence is shown to depend on the nearest-neighbor spin-spin correlations, which are readily probed in this experiment. We also extract the binding energy of the Zhang-Rice singlet and identify the Zhang-Rice triplet excitation in the RIXS spectra.

Figure 1

Schematic pictures of the creation of the ZR singlet (ZRS) excitons in the RIXS process. (a) Comparison of the RIXS initial and final states for the intrachain ZR singlet exciton, together with the corresponding energetic diagram. Full and empty symbols represent filled and empty states/orbitals. (b) A similar picture is shown for the case of the interchain ZR singlet exciton, for which the Li atom acts as a bridge between neighboring chains. The green arrow indicates the hole transfer between two plaquettes leading to excitonic excitations.

Figure 2

Incident-energy dependence of the RIXS spectra. XAS spectrum measured at the O $K$ edge on ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ with $\sigma$-polarized light and at 20 K (right side), together with the corresponding RIXS spectra (on an energy-loss scale) (left side) measured at incident photon energies given by the arrows relative to the XAS spectrum energy scale. The positions of the intra- and interchain ZR singlet excitations are emphasized by arrows. The position of the possible dispersive ZR fluorescence excitation is also shown by vertical lines (see text).

Figure 3

DFT and RIXS cluster calculations. (a) Calculated DOS within DFT+$U$ for the unoccupied states of ${\mathrm{Li}}_2{\mathrm{CuO}}_2$. The main panel shows the orbital-resolved DOS of ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ for $U_{3d}=5.5$ eV. The inset shows the variation in the total DOS for different values of $U_{3d}$ (the 0 eV reference energy is placed at the lower band edge of the unoccupied states). (b) Calculated XAS (inset) and RIXS for a ED cluster calculation based on two ${\mathrm{CuO}}_4$ plaquettes bridged by a Li atom. The red arrow indicates at which incident energy the RIXS spectrum has been calculated.

Figure 4

Temperature dependence of RIXS intensities of the intrachain and interchain ZR singlet excitations. RIXS spectra measured as a function of temperature at the O $K$ edge of ${\mathrm{Li}}_2{\mathrm{CuO}}_2$, with $\sigma$ polarization of light and an incident energy of (a) $\hslash {\omega }_i=530.1$ eV (on the edge of the UHB) and of (b) $\hslash {\omega }_i=531.9$ eV (on the Li-hybridized states). The RIXS spectra in (a) are normalized to the total intensity area of the $dd$ excitations [16]. (a),(b) The insets show different RIXS spectra, for which the spectrum at 300 K has been subtracted and the vertical continuous line indicates the energy position of the charge transfer energies ${\mathrm{\Delta }}_{inter,intra}$ (see text). (c),(d) The corresponding zoom on the ZR singlet excitons. The spectra are shifted in intensity by a constant offset for better visibility. (c) The inset shows the integrated RIXS intensity (normalized to 0.5 at room temperature) of the ZR singlet excitons as a function of temperature. Schematic energy scale for the (e) intrachain and (f) interchain ZR excitons, depicting how the ZR singlet excitation energy is shifted to energy losses lower than the charge transfer energy, $\mathrm{\Delta }$, by its binding energy, $B_{ZR}^{\left(s\right)}$, while the ZR triplet (ZRT) excitation energy is shifted above $\mathrm{\Delta }$. The splitting between the ZR singlet and ZR triplet excitation energies is $\mathrm{\Delta }{E}_{ZR}$.