  Two different ferroelectric materials, Sr$_{0.95}$Ba$_{0.05}$TiO$_3$ and
Sr$_{0.985}$Ca$_{0.015}$TiO$_3$, can be turned into polar metals with broken
centrosymmetry via electron doping. Systematic substitution of Nb$^{5+}$ for
Ti$^{4+}$ has revealed that these polar metals both commonly show a simple
superconducting dome with a single convex shape. Interestingly, the
superconducting transition temperature $T_\mathrm{c}$ is enhanced more strongly
in these polar metals when compared with the nonpolar matrix Sr(Ti,Nb)O$_3$.
The maximum $T_\mathrm{c}$ reaches 0.75K, which is the highest reported value
among the SrTiO$_3$-based families to date. However, the $T_\mathrm{c}$
enhancement is unexpectedly lower within the vicinity of the putative
ferroelectric quantum critical point. The enhancement then becomes much more
prominent at locations further inside the dilute carrier-density region, where
the screening is less effective. These results suggest that centrosymmetry
breaking, i.e., the ferroelectric nature, does not kill the superconductivity.
Instead, it enhances the superconductivity directly, despite the absence of
strong quantum fluctuations.
