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

TL;DR

This study investigates phonon behavior in HgBa$_2$CuO$_{4+\delta}$, revealing significant softening of the Cu-O bond stretching mode near the zone boundary, which is common among hole-doped high-$T_c$ cuprates and not linked to specific lattice distortions.

Contribution

It provides experimental evidence of phonon softening in HgBa$_2$CuO$_{4+\delta}$ and compares it with theoretical models, highlighting a common feature in hole-doped cuprates.

Findings

Cu-O bond stretching mode softens near zone boundary

Shell model describes low-energy phonons well

Softening is common in hole-doped high-$T_c$ cuprates

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.