Gapped sliding phononic modes in the incommensurate structure of the ladder-chain system Sr$_{14}$Cu$_{24}$O$_{41}$

We report on low energy Raman and infra-red (IR) excitations in Sr$_{14}$Cu$_{24}$O$_{41}$. Two modes are observed starting from room temperature in the 1-2 meV range. One is a fully symmetric Raman mode and the other, observed in c-axis reflectance, is an excitation carrying a dipole moment along the chain/ladder direction. We associate these modes with the gapped c-axis sliding motions of the charged, incommensurate CuO$_{2}$ chains and Sr$_{2}$Cu$_{2}$O$_{3}$ ladder layers. This approach is able to quantitatively explain the range and relative energies of these excitations which are sensitive probes of the charge and spin density-wave ordering in the ``14-24-41'' systems.