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Dynamic charge inhomogenity in cuprate superconductors

The inelastic x-ray scattering spectrum for phonons of $Δ_{1}$-symmetry including the CuO bond-stretching phonon dispersion is analyzed by a Lorentz fit in HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$, respectively, using recently calculated phonon frequencies as input parameters. The resulting mode frequencies of the fit are almost all in good agreement with the calculated data. An exception is the second highest $Δ_{1}$-branch compromising the bond-stretching modes which disagrees in both compounds with the calculations. This branch unlike the calculations shows an anomalous softening with a minimum around the wavevector $\vc{q}=\frac{2π}{a}(0.25, 0, 0)$. Such a disparity with the calculated results, that are based on the assumption of an undisturbed translation- and point group invariant electronic structure of the CuO plane, indicates some {\it static} charge inhomogenities in the measured probes. Most likely these will be charge stripes along the CuO bonds which have the strongest coupling to certain longitudinal bond-stretching modes that in turn selfconsistently induce corresponding {\it dynamic} charge inhomogenities. The symmetry breaking by the mix of dynamic and static charge inhomogenities can lead to a reconstruction of the Fermi surface into small pockets.