Electron-energy-loss and optical-transmittance investigation of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$

The energy-loss function Im(-1/ε) of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ has been measured over the range ${\mathit{E}}_{\mathrm{loss}}$=0.8 to 80 eV by transmission electron-energy-loss spectroscopy (EELS) (nonimaging). The energy and momentum resolution were 0.1 eV and 0.04 A${\mathrm{̊}}^{\mathrm{-}1}$, respectively. The low-energy spectra (${\mathit{E}}_{\mathrm{loss}}$≤3 eV) were studied as a function of momentum transfer (0.1 A${\mathrm{̊}}^{\mathrm{-}1}$≤q≤0.3 A${\mathrm{̊}}^{\mathrm{-}1}$). A well-defined peak in the loss function at ${\mathit{E}}_{\mathrm{loss}}$∼1 eV is observed to disperse with momentum proportional to ${\mathit{q}}^2$. This excitation is analyzed in terms of both an intracell, charge-transfer exciton model and the free-carrier (plasmon) model. The derived effective mass of the exciton ${\mathit{m}}_{\mathrm{tot}}$/m≃1.0 is far too small for a localized exciton. Using the free-carrier model and random-phase-approximation expressions for the dispersion coefficient, the carrier density and carrier effective mass can be determined separately. From our data and similar measurements by Nücker et al. [Phys. Rev. B 39, 12 379 (1989)], it is found that the effective mass roughly scales with carrier density. A heuristic model is introduced based on the assumption that low-energy gaps exist in portions of the Fermi surface due to structural instabilities. The model suggests how the effective mass could appear to scale with carrier density and why a single Drude term (with frequency-independent effective mass) does not describe the mid- to far-infrared optical spectra. Finally, the optical transmittance of the EELS sample was measured and the spectra analyzed in terms of the free-carrier model.