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The low energy lattice dynamics of the quasi-periodic spin-ladder cuprateSr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ are investigated using terahertz frequencysynchrotron radiation. A high density of low-lying optical excitations arepresent in the 1-3 THz energy range, while at least two highly absorbingexcitations stemming from rigid acoustic oscillations of the incommensuratechain and ladder sublattices, are observed at sub-terahertz frequencies. Theeffects of Ca substitution on the sub-terahertz quasi-acoustic sliding modegaps is investigated using coherent synchrotron radiation. Analysis of theresults suggest increasing substitution of Sr for Ca is accompanied by atransfer of spectral weight between sliding modes associated with differentchain-ladder dynamics. The observation is consistent with a transfer of holecharges from the chains to the ladders and modification of the sublatticedimensions following Ca substitution. The results are discussed in context tothe significance of low-lying vibrational dynamics and electron-phonon couplingin the superconducting state of certain quasi-periodic systems.

Effects of Ca substitution on quasi-acoustic sliding modes in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$