Acoustic plasmons and doping evolution of Mott physics in resonant inelastic x-ray scattering from cuprate superconductors

By incorporating a long-range Coulomb interaction into the framework of the one-band Hubbard model, we delineate how the low-energy plasmon around $1\mathrm{eV}$, which is a universal feature of the charge dynamics of the cuprates, manifests itself in the resonant inelastic x-ray scattering (RIXS) spectra. The long-range Coulomb interaction in the doped system controls the form of the intraband RIXS dispersion near the Brillouin zone center around the $\Gamma$ point. The out-of-plane momentum transfer component $q_z$ is found to play a key role in determining whether or not the RIXS spectrum shows a plasmon-related gap at $\Gamma$.

Figure 1

(Color online) Lowest-order Keldysh diagram for $K$-edge RIXS process, after Ref. 5.

Figure 2

(Color online) Calculated loss function for insulating SCOC as a function of energy transfer $\omega$ along the $\Gamma \text{−}(\pi ,0)\text{−}(\pi ,\pi )\text{−}\Gamma$ high symmetry line in the Brillouin zone. Results for two different model treatments of the Coulomb interaction are shown: (a) only the short-range onsite Hubbard $U$ term and (b) the full $V\left(q\right)$ of Eq. (9). Experimental plasmon dispersion obtained from EELS data (Ref. 3) is given by solid blue lines for reference in both panels (a) and (b). Note that intensities are plotted on a logarithmic scale.

Figure 3

(Color online) Calculated loss function for overdoped Bi2201 using four different ranges of the Coulomb potential, all restricted to $q_z=0$. Results in (a)–(d) are for an increasing range of the potential as follows: (a) only the onsite term $U$, (b) in-plane short-range term $V_{2\mathrm{D}}^{\mathit{sr}}$, (c) total in-plane term $V_{2\mathrm{D}}$, and (d) the full $V\left(q\right)$. The color scheme is the same as in Fig. 2.

Figure 4

(Color online) Calculated loss spectra for Bi2201 illustrating effect of $q_z$: (a) $q_z=2\pi ∕c$; (b) $q_z=0$. Blue solid lines show positions of the spectral peaks. The arrows show a peak position at $\Gamma$. The logarithmic color scale is the same as in Fig. 2.