Benoît Fauqué1, Shan Jiang1, Tom Fennell2, Bertrand Roessli2, Alexandre Ivanov3, Celine Roux-Byl4, Benoît Baptiste5, Philippe Bourges6, Kamran Behnia4, and Yasuhide Tomioka7
1 JEIP (USR 3573 CNRS), Collège de France, 75005 Paris, France
2 Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, Villigen, Switzerland
3 Institut Laue Langevin, 71 avenue des Martyrs, CS 20156, 38042 Grenoble Cedex, France
4 Laboratoire de Physique et d’Etude de Matériaux (CNRS) ESPCI Paris, Université PSL, 75005 Paris, France
5 IMPMC-Sorbonne Université and CNRS, 4, place Jussieu, 75005 Paris, France
6 Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
7 National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, 305-8565, Japan
Superconducting domes, ubiquitous across a variety of quantum materials, are often understood as a favored window for pairing opened by fluctuations of competing orders that induces a peak in the doping evolution of the superconducting transition. Yet, a quantitative understanding of how such a window closes remains lacking. Using inelastic neutron scattering (INS), we present a simple picture for the origin of the superconducting dome in electron-doped SrTiO3 [1].
In contrast to other families, the parent compound is not magnetic but instead is a quantum paraelectric. This state, characterized by a large dielectric constant (ε ≈ 20,000), arises from the softening of the zone-centered transverse optical (TO) phonon mode. By studying the evolution of the TO mode dispersion using cold and thermal triple-axis spectrometer, we are able to quantify—for the first time—the doping dependence of the dipolar correlation length (l0) (see figure), defined as the ratio of the velocity of the TO mode to its energy.
We find that the superconducting dome in strontium titanate terminates when l0 reaches its minimum possible value: the Ti–O bond distance (see figure). Moreover, the product of l0 and the Fermi wavevector (kF) peaks near the maximum critical temperature. This suggests that the superconducting dome in SrTiO3 arises from the interplay between the increase in the density of states and the inevitable collapse of the quantum paraelectric phase—both induced by doping.
The successful quantitative description of both the maximum and termination of the superconducting dome highlights the central role played by the soft ferroelectric mode in the pairing mechanism. This scenario may also apply to other quantum paraelectric materials, whether in bulk or at interfaces.
Figure: Doping evolution of l0=νTO/ωTO for Nb-doped (blue points) and La-doped (red points) (left scale). νTO and ωTO are directly measured by inelastic neutron scattering. The dashed line represents the Fermi surface wavevector kF (right scale). b) Product kF l0 versus doping. c) Doping evolution of the superconducting critical temperature (Tc). The end of the superconducting dome is concomitant with the saturation of l0 to about a/2 where a = 3.9 Å is the lattice parameter of SrTiO3.
[1] Benoît Fauqué et al, Nature Communications 16, 2301 (2025).