# Multiorbital Ferroelectric Superconductivity in doped SrTiO3

## TL;DR

This paper proposes that doped SrTiO$_3$ can host a unique ferroelectric superconducting state, stabilized by spin-orbit coupling mechanisms, and predicts a topological Weyl superconducting phase within it.

## Contribution

It introduces the concept of ferroelectric superconductivity in SrTiO$_3$ and elucidates the mechanisms stabilizing this phase through multiorbital analysis and spin-orbit coupling effects.

## Key findings

- Ferroelectric superconductivity is stabilized via Lifshitz transition at low carrier density.
- Magnetic field can induce ferroelectric superconductivity independently of carrier density.
- A topological Weyl superconducting state is predicted in the ferroelectric phase.

## Abstract

SrTiO$_3$ is a unique example of a system which exhibits both quantum paraelectricity and superconductivity. Thus, it is expected that the superconducting state is closely related to the intrinsic ferroelectric instability. Indeed, recent experiments suggest existence of a coexistent phase of superconductivity and ferroelectricity in Ca-substituted SrTiO$_3$. In this paper, we propose that SrTiO$_3$ can be a platform of the ferroelectric superconductivity, which is characterized by a ferroelectric transition in the superconducting state. By analyzing a multiorbital model for $t_{2g}$ electrons, we show that the ferroelectric superconductivity is stabilized through two different mechanisms which rely on the presence of the spin-orbit coupling. First, the ferroelectric superconducting state is stabilized in the dilute carrier density regime due to a ferroelectricity-induced Lifshitz transition. Second, it is stabilized under a magnetic field independent of the carrier density. The importance of the multiorbital or multiband nature for the ferroelectric superconductivity is clarified. Then, we predict a topological Weyl superconducting state in the ferroelectric superconducting phase of SrTiO$_3$.