A ferroelectric quantum phase transition inside the superconducting dome of Sr1−xCaxTiO3−δ

Abstract

SrTiO 3 , a quantum paraelectric 1 , becomes a metal with a superconducting instability after removal of an extremely small number of oxygen atoms 2 . It turns into a ferroelectric upon substitution of a tiny fraction of strontium atoms with calcium 3 . The two orders may be accidental neighbours or intimately connected, as in the picture of quantum critical ferroelectricity 4 . Here, we show that in Sr 1−x Ca x TiO 3−δ (0.002 < x < 0.009, δ < 0.001) the ferroelectric order coexists with dilute metallicity and its superconducting instability in a finite window of doping. At a critical carrier density, which scales with the Ca content, a quantum phase transition destroys the ferroelectric order. We detect an upturn in the normal-state scattering and a significant modification of the superconducting dome in the vicinity of this quantum phase transition. The enhancement of the superconducting transition temperature with calcium substitution documents the role played by ferroelectric vicinity in the precocious emergence of superconductivity in this system, restricting possible theoretical scenarios for pairing.A perovskite of the ABO 3 family, SrTiO 3 is a quantum paraelectric whose dielectric constant rises to ∼20,000 at low temperature 1 , but avoids long-range ferroelectric order. It becomes a metal by substituting Sr with La, Ti with Nb, or by removing O. It has been known for half a century that this metal is a superconductor at low temperatures 2 . More recently, a sharp Fermi surface and a superconducting ground state have been found to persist down to a carrier concentration of 10 17 cm −3 in SrTiO 3−δ (refs 5,6 However, mobile electrons screen polarization and therefore only insulating solids are expected to host a ferroelectric order. Hitherto, as a paradigm, ferroelectric quantum criticality, in contrast to its magnetic counterpart, was deprived of an experimental phase diagram in which a superconducting phase and a ferroelectric order share a common boundary.Here, we produce such a phase diagram in the case of Sr 1−x Ca x TiO 3−δ . The main new observations are the following: metallic Sr 1−x Ca x TiO 3−δ hosts a phase transition structurally indistinguishable from the ferroelectric phase transition in insulating Sr 1−x Ca x TiO 3 ; the coexistence between this ferroelectric-like order and superconductivity ends beyond a threshold carrier concentration; and, in the vicinity of this quantum phase transition, calcium substitution enhances the superconducting critical temperature and induces an upturn in the normal-state resistivity.Figure 1 summarizes what we know about the emergence of ferroelectricity, metallicity and superconductivity in this system. When a small fraction of Sr atoms (x > 0.002) is replaced with isovalent Ca, Sr 1−x Ca x TiO 3 becomes ferroelectric 3 , with a Curie temperature steadily increasing with Ca content in the dilute limit 0.002 < x < 0.02 (refs 3,13,14). Macroscopic polarization below the Curie temperature has been observed in dielectric and linear birefringence measurements, a...

Charge transport in a polar metal

“…1b-1d, 1f-1h and 1j-1l. Rischau et al found that in selected samples at x = 0.2% and 0.9%, this anomaly occurs close to where the structural phase transition was detected by Raman spectroscopy, sound velocity and thermal expansion measurements [21]. Most recently, thermal expansion measurements documented the evolution of the structural phase transition in Sr 1−x Ca x TiO 3−δ (x = 0.9%), starting from the insulating phase and extending deep into the metallic phase [34].…”

“…Nevertheless, it shows anomalies in various physical properties at the Curie temperature of the insulator. For example, Raman scattering found that the hardening of the FE soft mode in the dilute metal is indistinguishably similar to what is seen in the insulator [21]. The anomaly in resistivity was found to terminate at a threshold carrier density (n * ), near which the superconducting transition temperature was enhanced [21] providing evidence for a link between superconducting pairing and ferroelectricity, a subject of present attention [22][23][24][25][26][27][28][29][30][31][32].…”

“…The dilute metal undergoes a superconducting transition below 0.3 K [18][19][20]. Rischau et al have recently found that a superconducting phase coexists with a FE-like instability in ndoped Sr 1−x Ca x TiO 3−δ and superconductivity and ferroelectricity (FE) may be intimately linked [21]. The FE transition of insulating Sr 1−x Ca x TiO 3 was found to survive in metallic Sr 1−x Ca x TiO 3−δ .…”

Ferroelectric order versus metallicity in Sr1−xCaxTiO3−δ ( x<

“…Charge-carrier doping in pure SrTiO 3 by, e.g., a partial removal of oxygen or substitution of Sr (Ti) by La (Nb), induces metallic conductivity [22][23][24][25][26] and, for certain carrier concentrations, even superconductivity 27,28 . In systems with both, calcium substitution and electron doping (Sr 1−x Ca x TiO 3−δ ), the T C -related anomalies of the ferroelectric insulating parent compound persist within the metallic and superconducting phase 29,30 .…”

“…Rischau et al investigated the evolution of this ferroelectriclike transition with charge-carrier concentration n for Sr 1−x Ca x TiO 3−δ with x = 0.0022 and x = 0.009 30 . Based on minima in the resistivity data ρ(T ), a decreasing T C upon increasing n was derived and a disappearance of the ferroelectriclike phase above a critical carrier density n c that depends on the calcium content x.…”