Figure 1

(Color online) Lower panel: the optical scattering rate $1∕{\tau }^{\mathit{op}}\left(\omega \right)$ as a function of $\omega$ of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ at three doping levels. Solid lines are data and dashed lines are a fit using the Eliashberg formalism. We attribute the upturn in scattering below $50\mathrm{meV}$ to localization effects. The two top panels show the optical scattering rates of our two overdoped samples. They show no low-frequency localization effects.Reuse & Permissions

Figure 2

(Color online) The bosonic spectral density $I^2\chi \left(\omega \right)$ of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (a)–(c). The doping- and temperature-dependent bosonic function for three doping levels [$T_c=96\mathrm{K}$ (OPT96A), $82\mathrm{K}$ (OD82B), and $60\mathrm{K}$ (OD60G)]. At room temperature all samples exhibit a broad continuum background shown in panel (e). On lowering the temperature the broad background peak in the $300\text{−}\mathrm{K}$ spectrum evolves into a somewhat sharper low-energy peak with a deep valley above it. The spectral weight gained in the peak is roughly balanced by the spectral weight loss in the valley in all three samples. With increasing doping the intensity of the peak and intensity lost in the valley are significantly weakened [see Fig. 4b]. Panel (d) shows the temperature dependence of the frequency of the peak maximum in OPT96A marked by a star. Panel (f) shows the local magnetic susceptibility of underdoped Y-123 from neutron scattering (Refs. 5, 8, 36). While this is a different copper oxide system from the ones given in panels (a), (b), and (c) we note a qualitatively similar temperature evolution of panel (a).Reuse & Permissions

Figure 3

(Color online) The optical scattering rate for four different samples of optimally doped Bi2212. Dash-dotted line (red) from Homes (Ref. 41) dashed line (blue) from Tu et al.(Ref. 39), light solid line (purple) from van der (Ref. et al.[42]), and heavy solid line (black) from Hwang et al.(Ref. 26).Reuse & Permissions

Figure 4

(Color online) $T_c$-dependent properties of the peak and the valley (see text). (a) The central peak frequency is proportional to $T_c$, i.e., ${\Omega }_{\mathit{\text{peak}}}=8.0k_B{T}_c$, and the dashed line is a linear fit. (b) The peak and valley are closely connected, have a very similar $T_c$ dependence, and vanish at the same $T_c\approx 50\mathrm{K}$. The dashed lines are a linear fit. (c) The coupling constant ${\lambda }_{\mathit{\text{peak}}}$ vanishes at the same $T_c$ as the peak and valley. The dash-dotted line is obtained by using the linearly fitted center frequency [dashed line (a)] and the area under the peak [(b)], i.e., ${\lambda }_{\mathit{\text{peak}}}\simeq 2A_{\mathit{\text{peak}}}∕{\Omega }_{\mathit{\text{peak}}}$.Reuse & Permissions