Doping-Dependent Photon Scattering Resonance in the Model High-Temperature Superconductor ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ Revealed by Raman Scattering and Optical Ellipsometry

We study the model high-temperature superconductor ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ with electronic Raman scattering and optical ellipsometry over a wide doping range. The dependence of the resonant Raman cross section on the incident photon energy changes drastically as a function of doping, in a manner that corresponds to a rearrangement of the interband optical transitions seen with ellipsometry. This doping-dependent Raman resonance allows us to reconcile the apparent discrepancy between Raman and x-ray detection of magnetic fluctuations in superconducting cuprates. Intriguingly, the strongest variation occurs across the doping level where the antinodal superconducting gap appears to reach its maximum.

Figure 1

Raw Raman spectra for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.1}$ (a), (d), Hg1201 UD45 (b),(e), and UD94 (c),(f) obtained with 2.33 (a)–(c) and 1.96 eV (d)–(f) incident photons in the $B_{1g}$ scattering geometry. Data obtained on Si(100) surface are displayed for comparison (see text). The small feature in (b),(c) at $\sim 410\mathrm{meV}$ is due to fluorescence and/or an experiment artifact.

Figure 2

Difference between Raman susceptibility at 10 and 300 K measured with 1.96 incident photons in the $B_{1g}$ (a) and $B_{2g}$ (b) geometries, offset for clarity. Symbols indicate characteristic energies (see text). The bottom four spectra in (a) have been divided by a factor of 2 to allow a common scale.

Figure 3

Summary of ERS characteristic energies. Same symbols are used as in Fig. 2.

Figure 4

(a) Imaginary part of dielectric constant measured at 300 K. Inset: measurements at 10 K, where individual transitions are better seen (Fig. S5 in the Supplemental Material [27] shows the full temperature dependence). (b) Schematic of the $\alpha$ and $\delta$ transitions relative to our ERS photon energies. The two vertical lines for each incident-photon wavelength indicate the energies of the incident and scattered photons (after creating the two-magnon excitations). (c) Fit oscillator strength of the transitions labeled in (a) at 300 K. Other fit parameters are presented in Fig. S7 and Table I in the Supplemental Material [27].