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Doping-induced in-plane anisotropy of bond-stretching phonon softening in oxychloride <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ca</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>CuO</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> compounds
We measure the dispersion of the Cu-O bond-stretching phonon mode in the high-temperature superconducting parent compound Ca$_2$CuO$_2$Cl$_2$. Our density functional theory calculations predict a cosine-shaped bending of the dispersion along both the ($ξ$00) and ($ξξ$0) directions, while comparison with previous results on Ca$_{1.84}$CuO$_2$Cl$_2$ show it only along ($ξ$00), suggesting an …