#
Ferroelectricity, Superconductivity, and SrTiO_{3}—Passions of K.A. Müller

^{*}

## Abstract

**:**

## 1. Introduction

## 2. SrTiO${}_{3}$: Properties, Phase Diagram and Tuning Parameters

## 3. Superconductivity in Doped SrTiO${}_{3}$ from 1964 until 2020

## 4. Superconductivity in Two Dimensions

## 5. ${}^{18}$O Isotope Effect

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic phase diagram of SrTiO${}_{3}$ showing the ferroelectric (FE) and superconducting (SC) phases. Upon chemical substitution of Ca for Sr, i.e., Sr${}_{1-x}$Ca${}_{x}$TiO${}_{3}$ with $0.002<x<0.02$ [3], or by oxygen isotope substitution, i.e., SrTi${\left(\right)}_{{}^{\mathbf{18}}}$ with $y>0.33$ [4], the material develops a FE ground state beyond a quantum critical point (QCP). This FE phase occurs well below the structural transition from cubic to tetragonal [18]. Charge doping turns the material from an insulator (I) into a metal (M) at a critical carrier density (n${}_{\mathrm{MI}}$) of 10${}^{16}$ cm${}^{-3}$, while SC develops in a doping range n${}_{3\mathrm{D}}$ between 5 × 10${}^{17}$ and 10${}^{21}$ cm${}^{-3}$.

**Figure 2.**Growth and physical properties of LaAlO${}_{3}$/SrTi(${}^{18}$O${}_{y}^{16}$O${}_{1-y}$)${}_{3}$ interfaces. AFM images of the SrTiO${}_{3}$ substrate (

**a**) as-received, (

**b**) after the ${}^{18}$O${}_{y}$ substitution process, and (

**c**) after re-polishing and HF treatment (the size of all AFM images is 4 $\mathsf{\mu}$m × 4 $\mathsf{\mu}$m). (

**d**) RHEED signal during the growth of the LaAlO${}_{3}$ layer. One oscillation corresponds to the deposition of one unit cell of LaAlO${}_{3}$. (

**e**) Dielectric constant versus temperature of a SrTiO${}_{3}$ substrate ($y=0$) and of LaAlO${}_{3}$/SrTi(${}^{18}$O${}_{y}^{16}$O${}_{1-y}$)${}_{3}$ samples for different values of substitution. The dielectric properties have been measured in a homemade Helium cryostat using the Agilent E4980A Precision LCR Meter. The electric field was applied between the back electrode and the 2DES used as a top-electrode. (

**f**,

**g**) Sheet resistance versus temperature of the 2D electron system for ${}^{18}$O substituted samples. The resistance jump visible in the curve for y = 35% at ∼0.45 K is due to an electric spike, which occurred in the measurement system during our study.

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**MDPI and ACS Style**

Scheerer, G.; Boselli, M.; Pulmannova, D.; Rischau, C.W.; Waelchli, A.; Gariglio, S.; Giannini, E.; van der Marel, D.; Triscone, J.-M.
Ferroelectricity, Superconductivity, and SrTiO_{3}—Passions of K.A. Müller. *Condens. Matter* **2020**, *5*, 60.
https://doi.org/10.3390/condmat5040060

**AMA Style**

Scheerer G, Boselli M, Pulmannova D, Rischau CW, Waelchli A, Gariglio S, Giannini E, van der Marel D, Triscone J-M.
Ferroelectricity, Superconductivity, and SrTiO_{3}—Passions of K.A. Müller. *Condensed Matter*. 2020; 5(4):60.
https://doi.org/10.3390/condmat5040060

**Chicago/Turabian Style**

Scheerer, Gernot, Margherita Boselli, Dorota Pulmannova, Carl Willem Rischau, Adrien Waelchli, Stefano Gariglio, Enrico Giannini, Dirk van der Marel, and Jean-Marc Triscone.
2020. "Ferroelectricity, Superconductivity, and SrTiO_{3}—Passions of K.A. Müller" *Condensed Matter* 5, no. 4: 60.
https://doi.org/10.3390/condmat5040060