Single-Band Model of Resonant Inelastic X-Ray Scattering by Quasiparticles in High-$T_c$ Cuprate Superconductors

We show that a simple model of noninteracting quasiparticles accurately describes resonant inelastic x-ray scattering (RIXS) experiments in the hole-doped cuprate superconductors. Band structure alone yields signatures previously attributed to collective magnetic modes, such as the dispersing peaks and nontrivial polarization dependence found in several experiments. We conclude that RIXS data can be explained without positing the existence of magnetic excitations that persist with increasing doping. In so doing we develop a formalism for RIXS in itinerant electron systems that accounts for the positively charged core hole exactly and discover a mechanism by which the core hole produces polarization dependence mimicking that of a magnetic system.

Figure 1

Calculated (black curve) and experimental (Ref. [3], green dots) intensity vs energy transfer for spin-flip RIXS of optimally doped and overdoped Tl-2201 for antinodal momenta $\mathbf{Q}=q(\pi /a,0)$ exhibiting identical dispersing peaks. We subtracted a nonresonant elastic peak from the raw experimental data. We did not remove the contribution of $dd$ excitations, which accounts for the discrepancy at large $\mathrm{\Delta }\omega$.

Figure 2

Direct RIXS process that leaves behind a single particle-hole pair. The transient core hole potential can excite multiple particle-hole pairs.

Figure 3

Spin-flip ($\pi$-polarized) and non-spin-flip ($\sigma$-polarized) antinodal $\mathbf{Q}=0.80(\pi /a,0)$ line shapes of optimally doped ($p=0.15$) Bi-2212 for core hole potential $U_c=1.0\mathrm{eV}$. Blue: spin-flip channel/$\pi$ polarization; red: non-spin-flip channel/$\sigma$ polarization. Solid lines: calculated results; triangles, circles: $\pi$- and $\sigma$-polarized data from Ref. [35].

Figure 4

Calculated intensity vs energy transfer for spin-flip RIXS of optimally doped Bi-2212 ($p=0.15$) for antinodal momentum $\mathbf{Q}=(\pi /a,0)$ at incident energies 0, 0.2, and 0.4 eV above the absorption maximum. The increase in $\mathrm{\Delta }\omega$ with $\omega$ occurs when the RIXS final state belongs to the particle-hole continuum and does not occur if the final state is an excitation of a collective mode.