# A ferroelectric quantum phase transition inside the superconducting dome of Sr$_{1-x}$Ca$_{x}$TiO$_{3-\delta}$

## TL;DR

This study reveals a quantum phase transition inside the superconducting dome of Sr$_{1-x}$Ca$_{x}$TiO$_{3-eta}$, where ferroelectric order coexists with metallicity and influences superconductivity, highlighting the interplay between ferroelectricity and superconductivity.

## Contribution

It demonstrates the coexistence of ferroelectric order and superconductivity in Sr$_{1-x}$Ca$_{x}$TiO$_{3-eta}$ and identifies a quantum phase transition affecting the superconducting properties.

## Key findings

- Ferroelectric order coexists with metallicity and superconductivity.
- A quantum phase transition destroys ferroelectric order at a critical carrier density.
- Superconducting transition temperature is enhanced near the ferroelectric quantum critical point.

## Abstract

SrTiO$_{3}$, a quantum paraelectric, becomes a metal with a superconducting instability after removal of an extremely small number of oxygen atoms. It turns into a ferroelectric upon substitution of a tiny fraction of strontium atoms with calcium. The two orders may be accidental neighbors or intimately connected, as in the picture of quantum critical ferroelectricity. Here, we show that in Sr$_{1-x}$Ca$_{x}$TiO$_{3-\delta}$ ($0.002<x<0.009$, $\delta<0.001$) the ferroelectric order coexists with dilute metallicity and its superconducting instability in a finite window of doping. At a critical carrier density, which scales with the Ca content, a quantum phase transition destroys the ferroelectric order. We detect an upturn in the normal-state scattering and a significant modification of the superconducting dome in the vicinity of this quantum phase transition. The enhancement of the superconducting transition temperature with calcium substitution documents the role played by ferroelectric vicinity in the precocious emergence of superconductivity in this system, restricting possible theoretical scenarios for pairing.