Softening of Cu-O bond stretching phonon in tetragonal HgBa${}_2$CuO${}_{4+\delta }$

Abstract

Phonons in nearly optimally doped HgBa${}_2$CuO${}_{4+\delta }$ were studied by inelastic X-ray scattering. The dispersion of the low energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening towards the zone boundary, which deviates strongly from the model. This seems to be common in the hole-doped high-$T_{\mathrm{c}}$ superconducting cuprates, and, based on this work, not related to a lattice distortion specific to each material.

5 pages, 4 figures, accepted for publication in Phys. Rev. Lett