Abstract
Doped strontium titanate 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 is the role played by the proximity to a ferroelectric instability. In undoped STO, ferroelectric order can in fact be stabilized by substituting $^{16}$O with its heavier isotope $^{18}$O. Here we explore the superconducting properties of doped and isotope-substituted SrTi$(^{18}$O$_{y}^{16}$O$_{1-y})_{3-\delta}$ for $0\le y \le 0.81$ and carrier concentrations between $6\times 10^{17}$ and $2\times 10^{20}$ cm$^{-3}$ ($\delta<0.02$). We show that the superconducting $T_c$ increases when the $^{18}$O concentration is increased. For carrier concentrations around $5\times 10^{19}$~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 SrTi$^{18}$O$_3$ the maximum $T_c$ occurs at a much smaller carrier densities than for pure SrTi$^{16}$O$_3$. Our observations agree qualitatively with a scenario where superconducting pairing is mediated by fluctuations of the ferroelectric soft mode.
Highlights
Liquid helium does not become solid at ambient pressure, even for temperatures close to absolute zero
The advantage of the isotope substitution route is that the stoichiometry remains unaffected and modification of the electronic properties is fully obtained through quantum tuning of the zero-point fluctuations (ZPFs) amplitude
We provide a broad coverage of the two-dimensional parameter space of 18O isotope substitution and carrier density (6 × 1017–2 × 1021 cm−3) and show how the superconducting dome of STO changes as the system is tuned via 18O substitution across its quantum critical point (QCP) into the ferroelectric phase (33 at. % 18O for undoped STO)
Summary
Liquid helium does not become solid at ambient pressure, even for temperatures close to absolute zero. The material is instead observed to be a quantum paraelectric insulator with a large dielectric constant ( ∼ 104) as the ferroelectric ground state is suppressed by the ZPF of the oxygen atoms [2]. This is a quantum effect and the ZPF amplitude is controlled by h2/m where m is the ionic mass. We provide a broad coverage of the two-dimensional parameter space of 18O isotope substitution (up to 81%) and carrier density (6 × 1017–2 × 1021 cm−3) and show how the superconducting dome of STO changes as the system is tuned via 18O substitution across its quantum critical point (QCP) into the ferroelectric phase Our results challenge the concept of pairing mediated by phonons in the sense of bosonic particles, and require a generalization of the boson concept in the presence of strong anharmonicity
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