Electronic Raman scattering on out-of-plane disordered ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$: How the pseudogap affects the superconducting Raman response

We report Raman scattering measurements on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals with a different degree of out-of-plane disorder to examine the effect of $T_c$ change on the the electronic Raman response at the optimal doping level. The $B_{1g}$ peak energies for lower $T_c$ disordered samples are essentially independent of $T_c$. However, a further increase of $T_c$ by minimizing the degree of out-of-plane disorder leads to a high-energy shift of the $B_{1g}$ peak. Interestingly, abrupt change of the $B_{1g}$ peak energy occurs when the the superconducting gap energy exceeds the pseudogap energy, which results in the recovery of superconductivity-dominated Raman response in $B_{1g}$ symmetry. It suggests that these anomalous properties of the antinodal electrons are a consequence of the unconventional superconducting state of the cuprates where superconductivity coexists with the pseudogap in the ground state.

Figure 1

Superconducting transitions measured by magnetic susceptibility for ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{Ca}}_{1-y}{\mathrm{Y}}_y{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. For each crystal, $T_c$ is optimized by adjusting excess oxygen content $\delta$ under various annealing conditions. Inset: $T_c$ plotted against various annealing temperatures for ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Y}}_{0.08}{\mathrm{Ca}}_{0.92}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. Here the annealing at ${450}^{\circ }C$ gives the maximum $T_c$ of 96 K.

Figure 2

(a) and (b) $B_{2g}$ and $B_{1g}$ Raman response ${\chi }^{\prime \prime }\left(\omega \right)$ of Bi2212 with different Bi/Sr nonstoichiometry above and below $T_c$. (c) and (d) Raman spectra in the superconducting states in $B_{2g}$ and $B_{1g}$ symmetry measured at 10 K.

Figure 3

(a)–(c) Temperature evolution of the $B_{2g}$ Raman response ${\chi }^{\prime \prime }\left(\omega \right)$ for Bi2212 with different Bi/Sr nonstoichiometry above $T_c$. (d)–(f) Temperature evolution of the $B_{1g}$ Raman response ${\chi }^{\prime \prime }\left(\omega \right)$ for Bi2212 with different Bi/Sr nonstoichiometry above $T_c$. (g)–(i) $B_{1g}$ Raman response subtracted from one measured at 140 K. The black arrow indicates the pseudogap energy ${\omega }_{\text{PG}}$. (j)–(l) Temperature dependence of the spectral weight of $B_{1g}$ Raman response. The vertical dotted line indicates $T^{*}$.

Figure 4

Left: $B_{1g}$ Raman response subtracted from one measured at 140 K for Bi2212 with different Bi/Sr nonstoichiometry. The blue and red arrow indicate the position of the ${\omega }_{B_{1g}}$ and ${\omega }_{\text{PG}}$, respectively. Right: Schematic illustrations of angle dependence of the pseudogap (red line) and superconducting gap (blue line). The gap deviates from simple ${\mathit{d}}_{{\mathit{x}}^{\mathit{2}}-{\mathit{y}}^{\mathit{2}}}$-wave-like when ${\mathrm{\Delta }}^{*}$ becomes larger than $\mathrm{\Delta }.$