Description
The large-gap semiconductor strontium titanate ($SrTiO_3$)
becomes a metal upon removal of a tiny fraction of its oxygen
atoms. The dilute metal has a sharp Fermi surface and is
subject to a superconducting instability. Discovered half-a-
century ago, the superconducting dome of strontium titanate
remains doubly mysterious: How can superconductivity
persist when there is only one carrier for $10^5$ atoms and
the Fermi energy an order of magnitude smaller then than
the Debye energy? What destroys this cooperative order as
soon as carrier density exceeds 0.02 electrons per formula
unit? On the other hand, substituting strontium with calcium
stabilizes a long-range ferroelectric order in $Sr_{1-
x}Ca_xTiO_3$. We find that in $Sr_{1-x}Ca_xTiO_{3-
\delta}$ ferroelectricity coexists 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. This
happens at a critical doping level at which the Friedel
oscillations generated by neighboring dipoles interfere
destructively. In the vicinity of this quantum phase
transition, the superconducting critical temperature is
enhanced. We will discuss a possible link to ferroelectric
quantum criticality.
