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We report on a thermal-expansion study of the ferroelectric phase transitionin insulating Sr$_{1-x}$Ca$_x$TiO$_3$ ($x=0.009$) and its evolution uponincreasing charge-carrier concentration up to $n\simeq 60 \times10^{19}$cm$^{-3}$. Although electric polarization is screened by mobile chargecarriers, we find clear signatures of the ferroelectric phase transition in thethermal-expansion coefficient $\alpha$ of the weakly doped metallic samples.Upon increasing $n$, the transition temperature $T_\mathrm{C}(n)$ and themagnitude of the anomalies in $\alpha$ rapidly decrease up to a thresholdcarrier density $n^\star$ above which broadened anomalies remain present. Thereis no indication for a sign change of $\alpha$ as is expected for apressure-dependent quantum phase transition with $n$ as the control parameter.Thus, the ferroelectriclike transition is either continuously fading away or ittransforms to another low-temperature phase above $n^\star$, but this changehardly affects the temperature-dependent $\alpha(T)$ data.

Ferroelectric order versus metallicity in Sr$_{1-x}$Ca$_x$TiO$_{3-\delta}$ ($x=0.009$)