$\mathit{q}$ Dependence of Self-Energy Effects of the Plane Oxygen Vibration in YB${\mathrm{a}}_2$C${\mathrm{u}}_3$${\mathrm{O}}_7$

We have measured the temperature dependence of the peak position and linewidth of the 42.5 meV phonon branch in a twinned single crystal of YB${\mathrm{a}}_2$C${\mathrm{u}}_3$ ${\mathrm{O}}_7$ as a function of wave vector $\mathbf{q}$. In the $\left(100\right)/\left(010\right)$ direction in the Brillouin zone, considerable softening and broadening occur below the superconducting transition temperature $T_c$ at some values of $\mathbf{q}$. We observe an order of magnitude smaller softening and no linewidth broadening for $\mathbf{q}$ in the $\left(110\right)/\left(1\overline{1}0\right)$ direction. Possible implications of these findings for the symmetry of the superconducting order parameter are discussed.