Temperature dependence of the linewidths of the Raman-active phonons of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: Evidence for a superconducting gap between 440 and 500 ${\mathrm{cm}}^{\mathrm{-}1}$

The linewidths and frequencies of three Raman-active phonons have been measured in twin-free single crystals of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$. Below ${\mathit{T}}_{\mathit{c}}$, the phonon at 340 ${\mathrm{cm}}^{\mathrm{-}1}$ sharpens dramatically, the phonon at 440 ${\mathrm{cm}}^{\mathrm{-}1}$ sharpens slightly, and the phonon at 500 ${\mathrm{cm}}^{\mathrm{-}1}$ broadens. The temperature dependence of the phonon linewidths places the superconducting energy gap (2Δ) between 440 and 500 ${\mathrm{cm}}^{\mathrm{-}1}$, or 2Δ=6.8${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$–7.7${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$. Based upon the observed change in linewidth, the electron-phonon coupling strength of the 340-${\mathrm{cm}}^{\mathrm{-}1}$ phonon is estimated to be between 0.6 and 0.8.