Phonon self-energy effects due to superconductivity inBi2Sr2CaCu2O8+δ

Abstract

Raman scattering of ${A}_{1g}$ phonons in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals ($\ensuremath{\delta}=0.13,$ ${T}_{c}=86\mathrm{K}$) has been measured as a function of temperature. We report an anomalous softening in the frequency and a decrease in the linewidth of the ${A}_{1g}$ phonon at $290{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (${\mathrm{O}}_{1,2}$ $c$-axis in-phase vibration) below ${T}_{c}.$ We also confirm a smaller anomalous softening in the frequency of the ${A}_{1g}$ phonon at $465{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (${\mathrm{O}}_{3}$ $c$-axis vibration), but for this phonon mode no linewidth anomaly has been found. We compare the anomalous softening and linewidth behavior in the superconducting state with theoretical calculations for isotropic $s$-wave, planar $d$-wave, and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap symmetries and as for a layered superconductor model.