Figure 1

Raman response $R{\chi }^{\prime \prime }(\Omega ,T)$ (raw data): (a) and (b) $\left({\mathrm{Y}}_{0.92}{\mathrm{Ca}}_{0.08}\right){\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.3}$ (Y-UD28) and (c)–(h) ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\left({\mathrm{Ca}}_{1-\mathit{x}}{\mathrm{Y}}_{\mathit{x}}\right){\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (Bi-OPT94, Bi-OPT96, and Bi-OD87), in $B_{1g}$ and $B_{2g}$ symmetries as indicated. The corresponding light polarizations and sensitivities in the Brillouin zone are shown in the insets with copper and oxygen atoms displayed in red and blue, respectively. In (e), a double-headed arrow indicates the amplitude $A_{\mathrm{sc}}$ of the superconductivity-induced peak. Whenever applicable, a down-pointing arrow gives the approximate position where normal-state and superconducting spectra merge.Reuse & Permissions

Figure 2

Raman response $R{\chi }^{\prime \prime }(\Omega ,T)$ of ${\mathrm{Tl}}_2{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{6+\delta }$ with $T_c=78$ K (Tl-OD78) [panels (a) and (b)] and $T_c=46$ K (Tl-OD46) [panels (c) and (d)]. Note that the energy scales are different from those in Fig. 1. The spectra were measured with the laser line at 514 nm. The superconducting spectra were multiplied by constant scaling factors $s_0$ in the range $0.9⩽s_0⩽1.1$ to match the intensities above the pair-breaking range with those in the normal state.Reuse & Permissions

Figure 3

Normalized electronic Raman response ${\chi }_0^{\prime \prime }(\Omega ,p)$ (phonons subtracted) of $\left({\mathrm{Y}}_{1-\mathrm{y}}{\mathrm{Ca}}_{\mathrm{y}}\right){\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+\mathit{x}}$ in $B_{2g}$ symmetry (a), ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\left({\mathrm{Ca}}_{1-\mathit{x}}{\mathrm{Y}}_{\mathit{x}}\right){\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ in $B_{2g}$ (b), and $B_{1g}$ symmetry (c). Spectra from samples other than those shown in Fig. 1 are taken from our published work.[10, 14, 37, 53] For clarity, the phonons have been subtracted. The energy axes are normalized to the individual transition temperatures. All superconducting spectra merge with the normal-state response in the shaded range. The theoretical weak-coupling pair-breaking spectra (dashed lines) are the Tsuneto function on a realistic band structure weighted with the vertices for $B_{1g}$ and $B_{2g}$ symmetry. $2{\Delta }_0=9.3k_B{T}_c$ and a phenomenological broadening of 20% was used.Reuse & Permissions

Figure 4

Doping dependence of the superconductivity-induced features in Y-123 (full symbols), Bi-2212 (open symbols), HgBa${}_2$CuO${}_{4+\delta }$ (Hg-1201, crosses) and Tl-2201 in $B_{1g}$ symmetry (full circles). The data for Hg-1201 and those of Bi-2212 at $0.10⩽p⩽0.16$ (slightly smaller symbols) are taken from Ref.63. (a) Peak energies ${\Omega }_{\mathrm{peak}}$. ${\Omega }_{\mathrm{peak}}^{B2g}$ [the crosses are for Hg-1201, other symbols are given in panel (b)] is smaller than $2{\Delta }_0\left(p\right)=9.3k_B{T}_c^{\max }[1-82.6{(p-0.16)}^2]$ with $T_c^{\max }=94$ K (dashes). The same holds true for ${\Omega }_{\mathrm{peak}}^{B1g}$ (diamonds, circles and crosses) at $p>0.16$. A linear fit to the Bi-2212 data (straight full line) extrapolates to $p_{\mathrm{sc}2}\simeq 0.27$. (b) Amplitudes $A_{\mathrm{sc}}\left(p\right)$ in $B_{1g}$ and $B_{2g}$ symmetries (only our own data). The horizontal line at 1.03 cps/mW is the average of the amplitudes in $B_{2g}$ symmetry. (c) Inverse $B_{1g}$ amplitudes ${\left[A_{\mathrm{sc}}\left(p\right)\right]}^{-1}$ of Bi-2212, Y-123 and Tl-2201. The linear fit extrapolates to zero at $p\simeq 0.26$ close to $p_{\mathrm{sc}2}$.Reuse & Permissions

Figure 5

Energy and doping range of the superconductivity-induced $B_{1g}$ features for materials as indicated. The dashed line corresponds to $12k_B{T}_c$, where superconducting and normal-state spectra approximately merge as indicated in Figs. 1, 2, and 3. The black filled diamonds represent results of Raman measurements at high pressure (see Ref.40) with the doping calculated as described there (see text). All points for Hg-1201 and 3 points for Bi-2212 ($p=0.12,0.14,0.16$, black open diamonds) are taken from Ref.63. The lower (upper) envelope roughly corresponds to samples with lower (higher) defect concentration and/or internal strain. The shaded area indicates the doping range where the differences between normal-state and superconducting spectra fade away as observed for practically all homogeneous systems.[10, 14, 15, 16, 37, 52, 62, 63]Reuse & Permissions

Figure 6

Comparison of tunneling, ARPES, and Raman experiments with the tunneling and ARPES energy scales doubled. All open symbols correspond to Bi-2212. Tunneling results are plotted as open circles. They are compiled from Refs.8, 82, and 83 and labeled as A, Pa, and M, respectively. The stars represent the leading edge midpoints (LEM) measured above $T_c$ at the antinodal Fermi surface crossing and correspond to the pseudogap $2{\Delta }^{*}$ (T, Ref.31 and L, Ref.32). The pentagons correspond to the crossover temperatures $T^{*}$ (C, Ref.29) and are plotted in energy units as $6k_B{T}^{*}$. The down-pointing triangles represent the gap $2{\Delta }_0$ derived from ARPES as sketched in the inset according to Ref.9. The data are compiled from Refs.31, 32, 84, and 85. The up-pointing triangles represent $2{\Delta }_{\mathrm{sc}}=2{\Delta }_0{\ell }_{\mathrm{arc}}/{\ell }_{\mathrm{FS}}$, where ${\ell }_{\mathrm{arc}}$ is defined in the inset and ${\ell }_{\mathrm{FS}}$ is the full Fermi surface length (T, Ref.31 and L, Ref.32). On the overdoped side, ARPES results for Tl-2201 ($p=0.21$ and 0.25, triangles pointing to the left) are included (P, Ref.61). Here, the averages of the peak position and the LEM are shown, and the error is on the order of $\pm 20$%. The Raman data (approximate peak energies) correspond to those of the previous figures (N, O, V, B, Refs. 10, 14, 54 and 63). They are similar to within $\pm 20\%$ to those of earlier publications as summarized in Ref.42 and, more recently, Ref.63. The high-pressure results are taken from Ref.40 (G). The dash-dotted line is a fit to $6k_B{T}^{*}$ and $2{\Delta }^{*}$ in the range $p⩽0.16$.Reuse & Permissions

Figure 7

Dependence of the bound state's spectral weight on $E_b^0=(2{\Delta }_0-{\Omega }_{\mathrm{peak}}^{B1g})/k_B{T}_c$ of Bi-2212. The ranges close to optimal doping ($p=0.16\pm 0.01$) and at high doping ($p=0.22\pm 0.01$) are indicated. Here, the spectral weight is an integral over the in-gap mode alone after subtracting the weak-coupling pair-breaking response from the full response (see also Fig. 8). This can be directly derived from the data shown in Fig. 3c.Reuse & Permissions

Figure 8

Analysis of the spectral shape of the extra contribution to the superconducting $B_{1g}$ response in Bi-2212. The spectra are derived from those in Fig. 3c by subtracting the weak-coupling result [dashed line in Fig. 3c]. The solid line represents a Gaussian, the dashed one a Lorentzian. Except for the highest doping level of 0.23, all spectra are similarly well fit by Gaussians as the one at optimal doping.Reuse & Permissions