Superconductivity-induced resonant Raman scattering in multilayer high-T c superconductors

Resonant Raman scattering below ${T}_{c}$ has been discovered in several Bi-, Hg-, and Tl-based high-${T}_{c}$ superconductors with three or four ${\mathrm{CuO}}_{2}$ layers. For ${\mathrm{Bi}}_{2}{\mathrm{Si}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10+\ensuremath{\delta}},$ we found an unexpected crossover of the pair-breaking peak in the ${A}_{1g}$ spectrum from a broad bump at $\ensuremath{\Elzxh}\ensuremath{\omega}{=6k}_{B}{T}_{c}$ for ${E}_{\mathrm{exc}}=2.54\mathrm{eV}$ to a sharp peak at $\ensuremath{\Elzxh}\ensuremath{\omega}{=8k}_{B}{T}_{c}$ for ${E}_{\mathrm{exc}}=2.18\mathrm{eV},$ together with a strong enhancement of the Ca phonons. Under resonant conditions, the relative positions of the pair breaking peaks in ${A}_{1g},$ ${B}_{1g},$ and ${B}_{2g}$ channels are $2\ensuremath{\Delta}{(A}_{1g})=2\ensuremath{\Delta}{(B}_{1g})g2\ensuremath{\Delta}{(B}_{2g}).$ This relation implies that the ${A}_{1g}$ Raman channel is free from the Coulomb screening effect, just as predicted theoretically for a d-wave multilayer superconductor but have never been observed experimentally thus far. The observed resonance effect is evidence that the electronic state in the inner ${\mathrm{CuO}}_{2}$ planes is different from that of the outer ${\mathrm{CuO}}_{2}$ planes.