Raman-active phonons and mode softening in superconductingHgBa2CuO4+δ

Polarized micro-Raman spectra of a single crystallite of ${\mathrm{HgBa}}_2$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ have been measured and used to assign phonon modes of ${\mathit{A}}_{1\mathit{g}}$ and ${\mathit{E}}_{\mathit{g}}$ symmetry intrinsic to the superconducting phase. Predictions of the peak positions, linewidths, and Raman cross sections from compounds with similar bonding, i.e., HgO, Y-124, and Y-123, are closely matched and suggest assignments of the high-frequency ${\mathit{A}}_{1\mathit{g}}$ modes at 592 and 568 ${\mathrm{cm}}^{\mathrm{-}1}$ to apical oxygen stretch vibrations of the ideal structure and of a Cu or O defect (in the Hg plane). The low-frequency 168, 161, and 75 ${\mathrm{cm}}^{\mathrm{-}1}$ modes are assigned to O and Ba vibrations of ${\mathit{E}}_{\mathit{g}}$,${\mathit{A}}_{1\mathit{g}}$ and ${\mathit{E}}_{\mathit{g}}$ symmetry, respectively. An anomaly in the phonon frequency and linewidth of the 568-${\mathrm{cm}}^{\mathrm{-}1}$ ${\mathit{A}}_{1\mathit{g}}$ mode is observed below ${\mathit{T}}_{\mathit{c}}$. If interpreted as a change in the phonon self-energy due to the onset of superconductivity, this behavior is consistent with a gap energy near 568 ${\mathrm{cm}}^{\mathrm{-}1}$, i.e., 8.7${\mathit{kT}}_{\mathit{c}}$ in ${\mathrm{HgBa}}_2$ ${\mathrm{CuO}}_{4+\mathrm{\delta }}$ and constitutes a first estimate of the superconducting gap in this material. The Raman tensor elements for the assigned ${\mathit{A}}_{1\mathit{g}}$ and ${\mathit{E}}_{\mathit{g}}$ modes are given in absolute units.