Isotope tuning of the superconducting dome of strontium titanate

Doped strontium titanate ${\mathrm{SrTiO}}_3$ (STO) is one of the most dilute superconductors known today. The fact that superconductivity occurs at very low carrier concentrations is one of the two reasons that the pairing mechanism is not yet understood, the other being the role played by the proximity to a ferroelectric instability. In undoped STO, ferroelectric order can in fact be stabilized by substituting ${}^{16}\mathrm{O}$ with its heavier isotope ${}^{18}\mathrm{O}$. Here, we explore the superconducting properties of doped and isotope-substituted $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_{3-\delta }$ for $0\le y\le 0.81$ and carrier concentrations between $6\times {10}^{17}$ and $2\times {10}^{20}{\mathrm{cm}}^{-3}$ ($\delta <0.02$). We show that the superconducting $T_c$ increases when the ${}^{18}\mathrm{O}$ concentration is increased. For carrier concentrations around $5\times {10}^{19}{\mathrm{cm}}^{-3}$ this $T_c$ increase amounts to almost a factor 3, with $T_c$ as high as 580 mK for $y=0.74$. When approaching $\mathrm{SrTi}{}^{18}\mathrm{O}_3$ the maximum $T_c$ occurs at much smaller carrier densities than for pure $\mathrm{SrTi}{}^{16}\mathrm{O}_3$. Our observations agree qualitatively with a scenario where superconducting pairing is mediated by fluctuations of the ferroelectric soft mode.

Figure 1

Ferroelectricity in $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_3$. (a) Dielectric constant as a function of temperature. (b) Para-ferroelectric phase diagram including previous data by Itoh et al. [18]. (c) Low-temperature Raman spectra for $y=0.47$ showing the hardening of the ferroelectric soft mode below the $T_{Curie}$. (d) Temperature dependence of the Raman-detected soft mode for samples with $y=0.47$ (undoped and doped) and 0.74 (undoped) compared to hyper-Raman measurements for undoped $y=0$ [19].

Figure 2

Temperature dependence of resistivity. (a)–(d) Resistivity ${\rho }_{xx}$ as a function of $T$ and $T^2$ for samples with $y\approx 0.5$ and different $n$. For comparison, ${\rho }_{xx}$ of samples with $y=0$ and similar $n$ is shown as well as a function of $T^2$. (e) Temperature of the anomaly in resistivity associated with the polar order. Horizontal arrows mark $T_{Curie}$ measured on the insulating samples with the same ${}^{18}\mathrm{O}$ content. (f) Critical carrier density $n^{*}$ as a function of $y$.

Figure 3

Superconducting transitions. Superconducting transitions seen in resistivity measurements at selected carrier densities of (a) $3.2\times {10}^{18}$, (b) $1.1\times {10}^{19}$, (c) $4.8\times {10}^{19}$, and (d) $1.4\times {10}^{20}{\mathrm{cm}}^{-3}$ (see Appendix pp2 for all resistive transitions). (e) Superconducting transition seen by ac magnetic susceptibility and resistivity for $y=0.81$ and $n=1.2\times {10}^{19}{\mathrm{cm}}^{-3}$.

Figure 4

Superconducting phase diagrams. (a) Superconducting $T_c$ as a function of carrier density $n$. Dashed lines mark critical densities $n_{c1}$ and $n_{c2}$ at which the second and third band are filled, respectively [10, 20]. (b) Color plot showing the ferroelectric and the superconducting order as a function of $n$ and $y$. The gray line corresponds to the critical threshold $n^{*}$ [see Fig. 2]. (c) Normalized $T_c$ vs $1/{\epsilon }_0$ taken at low temperature on the insulating samples for oxygen-depleted $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_{3-\delta }$, ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_{3-\delta }$ (Ref. [21] and, in the interest of completeness, an extra measurement for $x=0.0022$), and ${\mathrm{SrTi}}_{0.98}{\mathrm{Nb}}_{0.02}{\mathrm{O}}_3$ under pressure [22]. Negative $1/{\epsilon }_0$ signifies that insulating samples ($\delta =0$) with the same $x$ or $y$ are ferroelectric. $T_c$ was normalized to the value obtained for $y=0$, $x=0$, or zero pressure.

Figure 5

Resistive superconducting transitions. Resistivity ${\rho }_{xx}$ as a function of temperature for all measured isotope-substituted $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_{3-\delta }$ samples.

Figure 6

Quantum oscillations measured in $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_{3-\delta }$ samples with (a), (b) $y=0.52$ and (c), (d) $y=0.81$ samples and different carrier densities at a temperature of 30 mK. (e) Oscillation frequencies $F$ as a function of carrier density $n$ compared to values measured by Lin et al. [9, 23] on unsubstituted $\mathrm{SrTi}{{}^{16}\mathrm{O}}_{3-\delta }(y=0)$.

Figure 7

(a) Low-temperature mobility $\mu$(2 K) as a function of carrier density for all samples. The data for $y=0$ are compared to data from Ref. [38] (measured at 4 K). (b) Mean free path $l$ as a function of carrier density. Arrows in both panels mark the critical carrier density $n^{*}$ shown in Fig. 2 of the main text.

Figure 8

Resistivity ${\rho }_{xx}$ (left-hand side) as well as its derivative $d{\rho }_{xx}/dT$ (right-hand side) of samples with an ${}^{18}\mathrm{O}$ content of $y=0.28$ at different carrier densities $n$.

Figure 9

Resistivity ${\rho }_{xx}$ (left-hand side) as well as its derivative $d{\rho }_{xx}/dT$ (right-hand side) of samples with an ${}^{18}\mathrm{O}$ content of $y=0.47$ or $y=0.52$ at different carrier densities $n$.

Figure 10

Resistivity ${\rho }_{xx}$ (left-hand side) as well as its derivative $d{\rho }_{xx}/dT$ (right-hand side) of samples with an ${}^{18}\mathrm{O}$ content of $y=0.74$ at different carrier densities $n$.

Figure 11

Resistivity ${\rho }_{xx}$ (left-hand side) as well as its derivative $d{\rho }_{xx}/dT$ (right-hand side) of samples with an ${}^{18}\mathrm{O}$ content of $y=0.81$ at different carrier densities $n$.