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Phonons in nearly optimally doped HgBa$_2$CuO$_{4+\delta}$ were studied byinelastic X-ray scattering. The dispersion of the low energy modes is welldescribed by a shell model, while the Cu-O bond stretching mode at high energyshows strong softening towards the zone boundary, which deviates strongly fromthe 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 latticedistortion specific to each material.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

physical review letters

Softening of Cu-O Bond Stretching Phonons in Tetragonal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow><mml:mi>HgBa</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:math>

Softening of Cu-O Bond Stretching Phonons in TetragonalHgBa2CuO4+δ