Resonant inelastic x-ray scattering study of the electronic structure of ${\text{Cu}}_2\text{O}$

A resonant inelastic x-ray scattering study of the electronic structure of the semiconductor cuprous oxide, ${\text{Cu}}_2\text{O}$, is reported. When the incident x-ray energy is tuned to the $\text{Cu}K$-absorption edge, large enhancements of the spectral features corresponding to the electronic transitions between the valence band and the conduction band are observed. A feature at 6.5 eV can be well described by an interband transition from occupied states of mostly $\text{Cu}3d$ character to unoccupied states with mixed $3d$, $4s$, and $\text{O}2p$ character. In addition, an insulating band gap is observed, and the momentum dependence of the lower bound is measured along the $\Gamma \text{−}R$ direction. This is found to be in good agreement with the valence-band dispersion measured with angle-resolved photoemission spectroscopy.

Figure 1

(Color online) Scattered intensity at $\mathbf{Q}\approx \left(201\right)$, plotted as a function of energy loss, $\hslash \omega$. The scans are shifted vertically for clarity. The incident energy for each scan can be read off from the vertical axis.

Figure 2

(Color online) Scattered intensity at $\mathbf{Q}\approx \left(201\right)$, plotted in pseudocolor intensity map. The horizontal axis is energy loss and the vertical axis the incident photon energy. The intensity scale bar is shown on the right. Note that the incident energies are higher than those in Fig. 1.

Figure 3

Energy-loss scan obtained with $E_i=8995.5$ and 9000.5 eV. The momentum is $\mathbf{Q}\sim \left(201\right)$. The open circles are experimental soft x-ray RIXS spectrum from Ref. 31. The solid line is a calculated RIXS spectrum from Ref. 31 scaled to match the current data.

Figure 4

(a) Schematic representation of experimental DOS from Ref. 34. The states shown here are mostly Cu states, except for the $\text{O}2p$ states. (b) Simplified band structure shown for illustrative purposes as described in the text. The arrows denote possible interband transitions with different momentum transfers. Vertical solid lines are $\mathbf{q}=0$ transitions; dashed lines correspond to $\mathbf{q}=\left(1/2,1/2,1/2\right)$ transitions. (c) Momentum dependence of the JDOS arising from the band structure shown in (b). Note that the magnitude of the momentum dependence of the lower bound of the interband transition continuum (thick solid line) mimics that of the valence band.

Figure 5

(Color online) RIXS intensity at different Q positions obtained with fixed incident energy at $E_i=8982.5\text{eV}$. The Q positions are along the $\Gamma \text{−}R$ line in reciprocal space, that is, along the $\left(1,\overline{1},1\right)$ direction. The inset shows the high-resolution data. The resolution function of 124 meV full width is shown as a solid line. Note that the weak feature at 1.3 eV observed in the main figure is an experimental artifact and is not observed in the high-resolution data.

Figure 6

(Color online) Intensity color map as a function of energy and momentum transfer. The intensity scale in counts per second is shown on the right-hand side of the main figure. Intensity of ten counts per second or higher is shown in brown. The dashed line is an empirical dispersion relation $2.15-0.25\text{cos}\left(2\pi q\right)$.