Long-range ferroelectric order is aborted in strontium titanate because of quantum fluctuations. As a consequence, the low-temperature static electric permittivity becomes extremely large and the effective Bohr radius of the order of a micron.  This is why removing a tiny fraction of oxygen atoms turns the system to a dilute metal, which has both a sharp Fermi surface and a superconducting instability [1].  Substituting strontium with calcium stabilizes a long-range ferroelectric order in Sr_1-xCa_xTiO₃ coexisting with metallicity and its superconducting instability in a narrow window of doping. As the carrier concentration is increased, the ferroelectric order is eventually destroyed by a quantum phase transition and the superconducting critical temperature is enhanced [2], providing support for a link between quantum-critical ferroelectricity and dilute superconductivity. The temperature dependence of resistivity is quadratic even in the absence of the two known mechanisms for generating T-square resitivity by electron-electron scattering [3]. Recent analysis points to the failure of Boltzmann-Drude picture of conductivity in explaining charge transport of this dilute metal [4].

[1] X. Lin et al., Phys. Rev. Lett. 112, 207002 (2014).

[2] C. W. Rischau et al., Nature Phys. 13, 643 (2017).

[3] X. Lin, B. Fauqué and K. Behnia, Science 349, 945 (2015) 

[4] X. Lin et al., NPJ Quantum Materials 2: 41 (2017).