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The influence of external pressure on the charge-density-wave (CDW) groundstate of the quasi-one-dimensional two-leg ladder compoundSr$_{10}$Ca$_{4}$Cu$_{24}$O$_{41}$ has been studied by optical reflectivitymeasurements as a function of temperature (10 - 300~K) and pressure $P$ (0.3 -4.3~GPa) over the spectral range 580 - 6000 cm$^1$. With increasing pressurethe CDW transition temperature $T_{CDW}$ decreases with the linear pressurecoefficient $\approx$-70~K/GPa, and above $\approx$3~GPa the CDW phase issuppressed at all temperatures. This behavior is similar to that in compoundsSr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ with increasing Ca content $x$ at ambientpressure, with the simple scaling $x \approx 3\cdot P(GPa)$. The size of theCDW gap decreases with increasing pressure, whereas the dimensionality of thehigh-temperature insulating phase in Sr$_{10}$Ca$_{4}$Cu$_{24}$O$_{41}$ withinthe ladder plane is hardly affected by external pressure.

Suppression of the Charge-Density-Wave State in Sr$_{10}$Ca$_{4}$Cu$_{24}$O$_{41}$ by External Pressure