Isotope effect in superconducting n-doped SrTiO3

Unidirectional Charge Orders Induced by Oxygen Vacancies on SrTiO3(001)

The discovery of high-mobility two-dimensional electron gas and low carrier density superconductivity in multiple SrTiO3-based heterostructures has stimulated intense interest in the surface properties of SrTiO3. The recent discovery of high-Tc superconductivity in the monolayer FeSe/SrTiO3 led to the upsurge and underscored the atomic precision probe of the surface structure. By performing atomically resolved cryogenic scanning tunneling microscopy/spectroscopy characterization on dual-TiO2-δ-terminated SrTiO3(001) surfaces with (√13 × √13), c(4 × 2), mixed (2 × 1), and (2 × 2) reconstructions, we disclosed universally broken rotational symmetry and contrasting bias- and temperature-dependent electronic states for apical and equatorial oxygen sites. With the sequentially evolved surface reconstructions and simultaneously increasing equatorial oxygen vacancies, the surface anisotropy reduces and the work function lowers. Intriguingly, unidirectional stripe orders appear on the c(4 × 2) surface, whereas local (4 × 4) order emerges and eventually forms long-range unidirectional c(4 × 4) charge order on the (2 × 2) surface. This work reveals robust unidirectional charge orders induced by oxygen vacancies due to strong and delicate electronic-lattice interaction under broken rotational symmetry, providing insights into understanding the complex behaviors in perovskite oxide-based heterostructures.

First-principles calculation of electron-phonon coupling in doped KTaO3

Background: Motivated by the recent experimental discovery of strongly surface-plane-dependent superconductivity at surfaces of KTaO 3 single crystals, we calculate the electron-phonon coupling strength, λ, of doped KTaO 3 along the reciprocal-space high-symmetry directions. Methods:Using the Wannier-function approach implemented in the EPW package, we calculate λ across the experimentally covered doping range and compare its mode-resolved distribution along the [001], [110] and [111] reciprocal-space directions. Results: We find that the electron-phonon coupling is strongest in the optical modes around the Γ point, with some distribution to higher k values in the [001] direction. The electron-phonon coupling strength as a function of doping has a dome-like shape in all three directions and its integrated total is largest in the [001] direction and smallest in the [111] direction, in contrast to the experimentally measured trends in critical temperatures. Conclusions: This disagreement points to a non-BCS character of the superconductivity. Instead, the strong localization of λ in the soft optical modes around Γ suggests an importance of ferroelectric soft-mode fluctuations, which is supported by our findings that the mode-resolved λ values are strongly enhanced in polar structures. The inclusion of spin-orbit coupling has negligible influence on our calculated mode-resolved λ values.

Synergetic Ferroelectricity and Superconductivity in Zero-Density Dirac Semimetals near Quantum Criticality

We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., Pb_{x}Sn_{1-x}Te, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

Superconductivity from energy fluctuations in dilute quantum critical polar metals

Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. Here we demonstrate that pairing mediated by energy fluctuations, ubiquitously present close to continuous phase transitions, occurs in dilute quantum critical polar metals and results in a dome-like dependence of the superconducting T_c on carrier density, characteristic of non-BCS superconductors. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optical phonons decouple from the electron charge. In the resulting vacuum, long-range attractive interactions emerge from the energy fluctuations of the critical phonons, resembling the gravitational interactions of a chargeless dark matter universe. Our estimates show that this mechanism may explain the critical temperatures observed in doped SrTiO₃. We provide predictions for the enhancement of superconductivity near polar quantum criticality in two- and three-dimensional materials that can be used to test our theory.

A large modulation of electron-phonon coupling and an emergent superconducting dome in doped strong ferroelectrics

We use first-principles methods to study doped strong ferroelectrics (taking BaTiO₃ as a prototype). Here, we find a strong coupling between itinerant electrons and soft polar phonons in doped BaTiO₃, contrary to Anderson/Blount’s weakly coupled electron mechanism for "ferroelectric-like metals”. As a consequence, across a polar-to-centrosymmetric phase transition in doped BaTiO₃, the total electron-phonon coupling is increased to about 0.6 around the critical concentration, which is sufficient to induce phonon-mediated superconductivity of about 2 K. Lowering the crystal symmetry of doped BaTiO₃ by imposing epitaxial strain can further increase the superconducting temperature via a sizable coupling between itinerant electrons and acoustic phonons. Our work demonstrates a viable approach to modulating electron-phonon coupling and inducing phonon-mediated superconductivity in doped strong ferroelectrics and potentially in polar metals. Our results also show that the weakly coupled electron mechanism for "ferroelectric-like metals” is not necessarily present in doped strong ferroelectrics.

Usually the coupling between polar phonons and itinerant electrons is weak in polar metals. Here, the authors show that in doped ferroelectrics (approximate polar metals), this coupling can be increased across the structural phase transition and as a result, phonon-mediated superconductivity emerges.

Ferroelectricity, Superconductivity, and SrTiO3—Passions of K.A. Müller

SrTiO3 is an insulating material which, using chemical doping, pressure, strain or isotope substitution, can be turned into a ferroelectric material or into a superconductor. The material itself, and the two aforementioned phenomena, have been subjects of intensive research of Karl Alex Müller and have been a source of inspiration, among other things, for his Nobel prize-winning research on high temperature superconductivity. An intriguing outstanding question is whether the occurrence of ferroelectricity and superconductivity in the same material is just a coincidence, or whether a deeper connection exists. In addition there is the empirical question of how these two phenomena interact with each other. Here we show that it is possible to induce superconductivity in a two-dimensional layer at the interface of SrTiO3 and LaAlO3 when we make the SrTiO3 ferroelectric by means of 18O substitution. Our experiments indicate that the ferroelectricity is perfectly compatible with having a superconducting two-dimensional electron system at the interface. This provides a promising avenue for manipulating superconductivity in a non centrosymmetric environment.

Superconductivity mediated by polar modes in ferroelectric metals

The occurrence of superconductivity in doped SrTiO₃ at low carrier densities points to the presence of an unusually strong pairing interaction that has eluded understanding for several decades. We report experimental results showing the pressure dependence of the superconducting transition temperature, T_c, near to optimal doping that sheds light on the nature of this interaction. We find that T_c increases dramatically when the energy gap of the ferroelectric critical modes is suppressed, i.e., as the ferroelectric quantum critical point is approached in a way reminiscent to behaviour observed in magnetic counterparts. However, in contrast to the latter, the coupling of the carriers to the critical modes in ferroelectrics is predicted to be small. We present a quantitative model involving the dynamical screening of the Coulomb interaction and show that an enhancement of T_c near to a ferroelectric quantum critical point can arise due to the virtual exchange of longitudinal hybrid-polar-modes, even in the absence of a strong coupling to the transverse critical modes.

Superconductivity in doped SrTiO₃ near to a ferroelectric quantum critical point emerges due to a strong interaction driving the formation of Cooper pairs, the nature of which has remained elusive for several decades.  Here, the authors reveal that pairing is due to the exchange of longitudinal hybrid polar modes rather than transverse critical modes.

Polar Nanodomains in a Ferroelectric Superconductor

The mechanisms by which itinerant carriers compete with polar crystal distortions are a key unresolved issue for polar superconductors, which offer new routes to unconventional Cooper pairing. Strained, doped SrTiO₃ films undergo successive ferroelectric and superconducting transitions, making them ideal candidates to elucidate the nature of this competition. Here, we reveal these interactions using scanning transmission electron microscopy studies of the evolution of polar nanodomains as a function of doping. These nanodomains are a precursor to the ferroelectric phase and a measure of long-range Coulomb interactions. With increasing doping, the magnitude of the polar displacements, the nanodomain size, and the Curie temperature are systematically suppressed. In addition, we show that disorder caused by the dopant atoms themselves presents a second contribution to the destabilization of the ferroelectric state. The results provide evidence for two distinct mechanisms that suppress the polar transition with doping in a ferroelectric superconductor.

Order-Disorder Ferroelectric Transition of Strained SrTiO_{3}

SrTiO_{3} is an incipient ferroelectric that is believed to exhibit a prototype displacive, soft mode ferroelectric transition when subjected to mechanical stress or alloying. We use high-angle annular dark-field imaging in scanning transmission electron microscopy to reveal local polar regions in the room-temperature, paraelectric phase of strained SrTiO_{3} films, which undergo a ferroelectric transition at low temperatures. These films contain nanometer-sized domains in which the Ti columns are displaced. In contrast, these nanodomains are absent in unstrained films, which do not become ferroelectric. The results show that the ferroelectric transition of strained SrTiO_{3} is an order-disorder transition. We discuss the impact of the results on the nature of the ferroelectric transition of SrTiO_{3}.

Ferroelectric Exchange Bias Affects Interfacial Electronic States

In polar oxide interfaces phenomena such as superconductivity, magnetism, 1D conductivity, and quantum Hall states can emerge at the polar discontinuity. Combining controllable ferroelectricity at such interfaces can affect the superconducting properties and sheds light on the mutual effects between the polar oxide and the ferroelectric oxide. Here, the interface between the polar oxide LaAlO₃ and the ferroelectric Ca-doped SrTiO₃ is studied by means of electrical transport combined with local imaging of the current flow with the use of scanning a superconducting quantum interference device (SQUID). Anomalous behavior of the interface resistivity is observed at low temperatures. The scanning SQUID maps of the current flow suggest that this behavior originates from an intrinsic bias induced by the polar LaAlO₃ layer. Such intrinsic bias combined with ferroelectricity can constrain the possible structural domain tiling near the interface. The use of this intrinsic bias is recommended as a method of controlling and tuning the initial state of ferroelectric materials by the design of the polar structure. The hysteretic dependence of the normal and the superconducting state properties on gate voltage can be utilized in multifaceted controllable memory devices.

Quantum critical phenomena in a compressible displacive ferroelectric

The dielectric and magnetic polarizations of quantum paraelectrics and paramagnetic materials have in many cases been found to initially increase with increasing thermal disorder and hence, exhibit peaks as a function of temperature. A quantitative description of these examples of "order-by-disorder" phenomena has remained elusive in nearly ferromagnetic metals and in dielectrics on the border of displacive ferroelectric transitions. Here, we present an experimental study of the evolution of the dielectric susceptibility peak as a function of pressure in the nearly ferroelectric material, strontium titanate, which reveals that the peak position collapses toward absolute zero as the ferroelectric quantum critical point is approached. We show that this behavior can be described in detail without the use of adjustable parameters in terms of the Larkin-Khmelnitskii-Shneerson-Rechester (LKSR) theory, first introduced nearly 50 y ago, of the hybridization of polar and acoustic modes in quantum paraelectrics, in contrast to alternative models that have been proposed. Our study allows us to construct a detailed temperature-pressure phase diagram of a material on the border of a ferroelectric quantum critical point comprising ferroelectric, quantum critical paraelectric, and hybridized polar-acoustic regimes. Furthermore, at the lowest temperatures, below the susceptibility maximum, we observe a regime characterized by a linear temperature dependence of the inverse susceptibility that differs sharply from the quartic temperature dependence predicted by the LKSR theory. We find that this non-LKSR low-temperature regime cannot be accounted for in terms of any detailed model reported in the literature, and its interpretation poses an empirical and conceptual challenge.

Terahertz field-induced ferroelectricity in quantum paraelectric SrTiO3

"Hidden phases" are metastable collective states of matter that are typically not accessible on equilibrium phase diagrams. These phases can host exotic properties in otherwise conventional materials and hence may enable novel functionality and applications, but their discovery and access are still in early stages. Using intense terahertz electric field excitation, we found that an ultrafast phase transition into a hidden ferroelectric phase can be dynamically induced in quantum paraelectric strontium titanate (SrTiO₃). The induced lowering in crystal symmetry yields substantial changes in the phonon excitation spectra. Our results demonstrate collective coherent control over material structure, in which a single-cycle field drives ions along the microscopic pathway leading directly to their locations in a new crystalline phase on an ultrafast time scale.

Multiferroics beyond electric-field control of magnetism

Multiferroic materials, with their combined and coupled magnetism and ferroelectricity, provide a playground for studying new physics and chemistry as well as a platform for the development of novel devices and technologies. Based on my July 2017 Royal Society Inaugural Lecture, I review recent progress and propose future directions in the fundamentals and applications of multiferroics, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism.

Enhancing superconductivity in SrTiO3 films with strain

The nature of superconductivity in SrTiO₃, the first oxide superconductor to be discovered, remains a subject of intense debate several decades after its discovery. SrTiO₃ is also an incipient ferroelectric, and several recent theoretical studies have suggested that the two properties may be linked. To investigate whether such a connection exists, we grew strained, epitaxial SrTiO₃ films, which are known to undergo a ferroelectric transition. We show that, for a range of carrier densities, the superconducting transition temperature is enhanced by up to a factor of two compared to unstrained films grown under the same conditions. Moreover, for these films, superconductivity emerges from a resistive state. We discuss the localization behavior in the context of proximity to ferroelectricity. The results point to new opportunities to enhance superconducting transition temperatures in oxide materials.

Multiferroic quantum criticality

The zero-temperature limit of a continuous phase transition is marked by a quantum critical point, which can generate physical effects that extend to elevated temperatures. Magnetic quantum criticality is now well established, and has been explored in systems ranging from heavy fermion metals to quantum Ising materials. Ferroelectric quantum critical behaviour has also been recently demonstrated, motivating a flurry of research investigating its consequences. Here, we introduce the concept of multiferroic quantum criticality, in which both magnetic and ferroelectric quantum criticality occur in the same system. We develop the phenomenology of multiferroic quantum criticality and describe the associated experimental signatures, such as phase stability and modified scaling relations of observables. We propose several material systems that could be tuned to multiferroic quantum criticality utilizing alloying and strain as control parameters. We hope that these results stimulate exploration of the interplay between different kinds of quantum critical behaviours.

Enhanced superconductivity close to a non-magnetic quantum critical point in electron-doped strontium titanate

Studies on quantum critical points (QCP) have focused on magnetic QCPs to date. Remarkable phenomena such as superconductivity due to avoided criticality have been discovered, but we focus here on the non-magnetic counterpart, i.e., the superconductivity of SrTiO3 regarded as being close to a ferroelectric QCP. Here we prepare high-quality Sr1-xLaxTi(16O1-z18Oz)3 single crystals without localisation at low temperatures, which allow us to systematically investigate the La substitution of Sr as an alternative to introducing oxygen vacancies. Analysis of our data based on a theoretical model predicts an appearance of the ferroelectric QCP around 3 × 1018 cm-3. Because of the QCP, the superconducting dome of Sr1-xLaxTiO3 can be raised upwards. Furthermore, remarkable enhancement of Tc (~0.6 K) is achieved by 18O exchange on the Sr1-xLaxTiO3 crystals. These findings provide a new knob for observing intriguing physics around the ferroelectric QCP.

Single-Gap Superconductivity and Dome of Superfluid Density in Nb-Doped SrTiO_{3}

SrTiO_{3} exhibits a superconducting dome upon doping with Nb, with a maximum critical temperature T_{c}≈0.4  K. Using microwave stripline resonators at frequencies from 2 to 23 GHz and temperatures down to 0.02 K, we probe the low-energy optical response of superconducting SrTiO_{3} with a charge carrier concentration from 0.3 to 2.2×10^{20}  cm^{-3}, covering the majority of the superconducting dome. We find single-gap electrodynamics even though several electronic bands are superconducting. This is explained by a single energy gap 2Δ due to gap homogenization over the Fermi surface consistent with the low level of defect scattering in Nb-doped SrTiO_{3}. Furthermore, we determine T_{c}, 2Δ, and the superfluid density as a function of charge carrier concentration, and all three quantities exhibit the characteristic dome shape.

Physics of SrTiO3-based heterostructures and nanostructures: a review

This review provides a summary of the rich physics expressed within SrTiO3-based heterostructures and nanostructures. The intended audience is researchers who are working in the field of oxides, but also those with different backgrounds (e.g., semiconductor nanostructures). After reviewing the relevant properties of SrTiO3 itself, we will then discuss the basics of SrTiO3-based heterostructures, how they can be grown, and how devices are typically fabricated. Next, we will cover the physics of these heterostructures, including their phase diagram and coupling between the various degrees of freedom. Finally, we will review the rich landscape of quantum transport phenomena, as well as the devices that elicit them.

Prospects and applications near ferroelectric quantum phase transitions: a key issues review

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T _c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.