Polarization-dependent infrared reflectivity study of Sr$_{2.5}$Ca$_{11.5}$Cu$_{24}$O$_{41}$ under pressure: Charge dynamics, charge distribution, and anisotropy

We present a polarization-dependent infrared reflectivity study of the spin-ladder compound Sr$_{2.5}$Ca$_{11.5}$Cu$_{24}$O$_{41}$ under pressure. The optical response is strongly anisotropic, with the highest reflectivity along the ladders/chains (\textbf{E}$\|$c) revealing a metallic character. For the polarization direction perpendicular to the ladder plane, an insulating behavior is observed. With increasing pressure the optical conductivity for \textbf{E}$\|$c shows a strong increase, which is most pronounced below 2000~cm$^{-1}$. According to the spectral weight analysis of the \textbf{E}$\|$c optical conductivity the hole concentration in the ladders increases with increasing pressure and tends to saturate at high pressure. At $\sim$7.5~GPa the number of holes per Cu atom in the ladders has increased by $\Delta \delta$=0.09 ($\pm$0.01), and the Cu valence in the ladders has reached the value +2.33. The optical data suggest that Sr$_{2.5}$Ca$_{11.5}$Cu$_{24}$O$_{41}$ remains electronically highly anisotropic up to high pressure, also at low temperatures.