Analysis of resonant inelastic x-ray scattering in ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$

We provide a semiquantitative explanation of a recent experiment on the resonant inelastic x-ray scattering (RIXS) in insulating cuprate ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ [Y. J. Kim et al., Phys. Rev. Lett. 89, 177003 (2002)]. We show theoretically that there are three characteristic peaks in RIXS spectra, two of which are attributed to the charge transfer excitation and are reasonably assigned to those observed experimentally. The lowest-energy peak has a relatively large dispersion $(\sim 0.8\mathrm{eV})$ and is suppressed near the zone corner $(\pi ,\pi )$, in agreement with the experiment. We stress that electron correlation is an essential factor for explaining the overall energy-momentum dependence of the RIXS spectra consistently.

Figure 1

RIXS spectra obtained by Kim et al. are shown for various momentum transfers as a function of energy transfer. (Reproduced from Ref. 5.)

Figure 2

(a) Diagram for the transition probability in the RIXS process. Green’s functions for Cu $1s$, $4p$, and $3d$ electrons are assigned to the solid lines labeled $1s$, $4p$, and $3d$, respectively. The wavy and broken lines represent the photon propagator and core hole potential $V$, respectively. The shaded triangle is the effective scattering vertex renormalized by Coulomb interaction $U_{dd}$. (b) Vertex renormalization in the RPA. The empty square represents antisymmetrized bare Coulomb interaction between Cu $3d$ electrons.

Figure 3

The upper figures show the $\mathrm{Cu}\mathrm{O}$ plaquette and the contour in the first Brillouin zone (BZ). The lower six panels show the RIXS spectra as a function of the energy loss $\omega ={\omega }_i-{\omega }_f$ on the above contour in the BZ. The thick solid (thin broken) curves are results obtained with (without) RPA vertex renormalization.

Figure 4

The total density of states and the Cu $3d_{x^2-y^2}$ partial density of states are shown by the solid and broken lines, respectively. The inset shows the band dispersion of the model in HF theory.

Figure 5

Left panel shows details of the spectra along the line $(0,0)\text{−}(\pi ,0)$ for $\omega =2–3\mathrm{eV}$. The data are offset vertically, and the thick horizontal bars drawn on the left vertical axis denote the baseline for each spectrum. The arrows denote the positions of the main peak. Right panel shows the position of the main peak as a function of $\mathbf{q}$.