Superconductivity

Ferroelectricity woos pairing

Ferroelectricity and superconductivity do not have much in common. Now, a superconducting and a ferroelectric-like state have been found to coexist in a doped perovskite oxide.

Can ferroelectricity and superconductivity occur simultaneously? Can ferroelectricity boost the superconducting critical temperature? Writing in Nature Physics, Carl Rischau and colleagues1 report experimental results suggesting that the coexistence of a ferroelectric-like state and superconductivity may be possible.

Ferroelectricity usually originates from a structural instability in a material with a high-temperature, inversion-symmetric, dielectric insulating phase. Below a critical temperature — the Curie temperature TC — a structural transition takes place: the compound's symmetry lowers and is no longer centrosymmetric, leading to a macroscopic polarization that can be reversed by an electric field. Superconductivity is often found in metallic systems below a critical temperature Tc at which electrons form Cooper pairs and condense, leading to a zero-resistance state and magnetic flux expulsion (the so-called Meissner effect).

The stability of a polar metallic state was first proposed in 1965 by Philip Anderson2. Experimental evidence of such a state has been scarce; recent 'sightings' involved doped BaTiO3 surfaces3 and (111) LaNiO3 films4. Yet the coexistence of superconductivity and ferroelectricity would still come as a surprise, since the two phases do not seem to have much in common.

Enter SrTiO3, a widely studied insulating compound experiencing an enduring fascination from the condensed-matter community. This strong interest stems partly from the fact that SrTiO3 is on the verge of a ferroelectric instability. The variation of its static dielectric constant on lowering the temperature is similar to that of a ferroelectric material, with a divergence taking place at TC, but it does not become infinite; it ultimately levels off at very low temperature to a value in excess of 25,000 (the dielectric constant of silicon dioxide is about 4).

Quantum fluctuations can account for such behaviour: they prevent a macroscopic polarization from developing since the barrier between the two equivalent free-energy minima of the ferroelectric double well is too small to prevent tunnelling between the 'up' and 'down' polar states (Fig. 1). Strain, very small isovalent Ca doping, or substitution of 16O with 18O atoms are all able to turn SrTiO3 into a ferroelectric.

Figure 1: Energy versus polarization as a function of a tuning parameter.
figure1

Energy versus polarization as a function of a tuning parameter. When approaching the quantum critical point (QCP), for a particular value of the tuning parameter, the system is in a 'quantum paraelectric state': the double well is not deep enough to allow for a stable polarization (ferroelectric state) to develop. Ca-doping, the tuning mechanism used by Rischau et al.1, drives SrTiO3 from a quantum paraelectric state to a ferroelectric state.

SrTiO3 can also be doped with electrons by replacing Sr with La, Ti with Nb, or reducing the oxygen content. SrTiO3 then becomes conducting and superconducting at very low electronic densities (of the order of 1017 cm−3). This low-density conduction is linked to the large dielectric constant and concomitant large Bohr radius that prevents electron localization. These two ordered states, ferroelectricity and superconductivity, are thus not 'far' from the pristine SrTiO3 ground state.

Rischau and colleagues have now studied SrTiO3 crystals that are not only oxygen-deficient — that is, electron-doped and hence superconducting — but also weakly doped with Ca (enabling a ferroelectric-like state to develop). Measurements of thermal expansion, sound velocity and resistivity show that, in some doping range, superconducting crystals display signatures of a structural phase transition similar to the typical ferroelectric transition seen in insulating, undoped crystals. Anomalies at the phase-transition temperature in the resistivity suggest a coupling of the structural transition to the electronic system.

The authors mapped out a temperature-versus-carrier concentration phase diagram, featuring a region where the superconducting and 'ferroelectric' states coexist, and established a correspondence between the level of doping (oxygen vacancies or calcium) and the carrier concentration. (Quotation marks for the term ferroelectric are in order since the polarization cannot be switched in the metallic phase.)

Further studies are needed for elucidating the role of Ca doping on the structure and electronic properties of SrTiO3. One may wonder, for instance, whether Ca doping, which lowers the local crystal symmetry, causes couplings to other modes that may mix orbital states. Also, does Ca doping change the level of correlations and the bandwidth of the system (the latter being related to orbital overlap), possibly requiring the introduction of an extra scale in the phase diagram in addition to that pertaining to electron and Ca doping?

An interesting observation is that for a range of values of carrier densities in the region of overlapping orders, the superconducting critical temperature Tc is higher for Ca-doped crystals than for undoped samples, suggesting that ferroelectricity may boost Tc.

The possible role of ferroelectric quantum fluctuations on superconductivity in SrTiO3 has recently been discussed by Jonathan Edge and colleagues5. The general idea is that close to a quantum critical point, where different phases compete, one is left with low-energy excitations. Any residual interactions may then drive the system to a superconducting state. For SrTiO3, Ca-doping, 18O substitution or straining the lattice brings the system closer to ferroelectricity — and hence closer to a quantum critical point.

For SrTiO3, the picture proposed by Edge et al. is that superconductivity appears in the underdoped regime when the Fermi surface forms and disappears in the overdoped regime when one is moving away from quantum criticality. The prediction for 18O-substituted SrTiO3 is that Tc should be higher with a maximum critical temperature shifted to lower doping as compared to 16O-SrTiO3. Recent experiments6 indeed seem to point to a higher Tc for O18-SrTiO3.

Doping reduces the height of the barrier separating the two free-energy minima and thus promotes quantum fluctuations that rapidly destroy the ferroelectric-like state. As found by Rischau et al., the coexistence of superconductivity and ferroelectricity is indeed restricted to a small region at low doping levels. In this region, the material is a superconductor with broken spatial inversion symmetry — a special class of superconductors that have attracted a lot of attention and whose order parameter should display a non-trivial symmetry7.

Finally, what about the celebrated LaAlO3/SrTiO3 system? At its interface, superconductivity has been observed with a dome-shaped phase diagram8, which is, however, different that of bulk-doped SrTiO3 (ref. 9). Is the LaAlO3/SrTiO3 phase diagram modified and/or is Tc enhanced if 18O-SrTiO3 or Ca-doped SrTiO3 are used? What about the breaking of inversion symmetry, also observed at the LaAlO3/SrTiO3 interface, and its impact on superconductivity? Further experiments on the LaAlO3/SrTiO3 interface and doped SrTiO3 crystals will hopefully soon answer some of the fascinating questions raised by the findings of Rischau and colleagues.

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Correspondence to Marc Gabay or Jean-Marc Triscone.

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Gabay, M., Triscone, JM. Ferroelectricity woos pairing. Nature Phys 13, 624–625 (2017). https://doi.org/10.1038/nphys4124

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