Quantum Critical Origin of the Superconducting Dome in SrTiO_{3}

Electronic-grade epitaxial (111) KTaO3 heterostructures

KTaO3 heterostructures have recently attracted attention as model systems to study the interplay of quantum paraelectricity, spin-orbit coupling, and superconductivity. However, the high and low vapor pressures of potassium and tantalum present processing challenges to creating heterostructure interfaces clean enough to reveal the intrinsic quantum properties. Here, we report superconducting heterostructures based on high-quality epitaxial (111) KTaO3 thin films using an adsorption-controlled hybrid PLD to overcome the vapor pressure mismatch. Electrical and structural characterizations reveal that the higher-quality heterostructure interface between amorphous LaAlO3 and KTaO3 thin films supports a two-dimensional electron gas with substantially higher electron mobility, superconducting transition temperature, and critical current density than that in bulk single-crystal KTaO3-based heterostructures. Our hybrid approach may enable epitaxial growth of other alkali metal-based oxides that lie beyond the capabilities of conventional methods.

Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.

Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

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.

Tunable superconductivity and its origin at KTaO3 interfaces

What causes Cooper pairs to form in unconventional superconductors is often elusive because experimental signatures that connect to a specific pairing mechanism are rare. Here, we observe distinct dependences of the superconducting transition temperature T_c on carrier density n_2D for electron gases formed at KTaO₃ (111), (001) and (110) interfaces. For the (111) interface, a remarkable linear dependence of T_c on n_2D is observed over a range of nearly one order of magnitude. Further, our study of the dependence of superconductivity on gate electric fields reveals the role of the interface in mediating superconductivity. We find that the extreme sensitivity of superconductivity to crystallographic orientation can be explained by pairing via inter-orbital interactions induced by an inversion-breaking transverse optical phonon and quantum confinement. This mechanism is also consistent with the dependence of T_c on n_2D. Our study may shed light on the pairing mechanism in other superconducting quantum paraelectrics.

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.

Simultaneous Imaging of Dopants and Free Charge Carriers by Monochromated EELS

Doping inhomogeneities in solids are not uncommon, but their microscopic observation and understanding are limited due to the lack of bulk-sensitive experimental techniques with high enough spatial and spectral resolution. Here, we demonstrate nanoscale imaging of both dopants and free charge carriers in La-doped BaSnO₃ (BLSO) using high-resolution electron energy-loss spectroscopy (EELS). By analyzing high- and low-energy excitations in EELS, we reveal chemical and electronic inhomogeneities within a single BLSO nanocrystal. The inhomogeneous doping leads to distinctive localized infrared surface plasmons, including a previously unobserved plasmon mode that is highly confined between high- and low-doping regions. We further quantify the carrier density, effective mass, and dopant activation percentage by EELS and transport measurements on the bulk single crystals of BLSO. These results not only represent a practical approach for studying heterogeneities in solids and understanding structure-property relationships at the nanoscale, but also demonstrate the possibility of infrared plasmon tuning by leveraging nanoscale doping texture.

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.

Enhanced superconductivity and ferroelectric quantum criticality in plastically deformed strontium titanate

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach using irreversible, plastic deformation of single crystals. We show that compressive plastic deformation induces low-dimensional superconductivity well above the superconducting transition temperature (T_c) of undeformed SrTiO₃, with evidence of possible superconducting correlations at temperatures two orders of magnitude above the bulk T_c. The enhanced superconductivity is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe deformation-induced signatures of quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order using Raman scattering. Our results suggest that strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence T_c, consistent with a theory of superconductivity enhanced by soft polar fluctuations. Our results demonstrate the potential of plastic deformation and dislocation engineering for the manipulation of electronic properties of quantum materials.

Quantum Buckling in Metal-Organic Framework Materials

Metal-organic frameworks are porous materials composed of metal ions or clusters coordinated by organic molecules. As a response to applied uniaxial pressure, molecules with a straight shape in the framework start to buckle. At sufficiently low temperatures, this buckling has a quantum nature described by a superposition of degenerate buckling states. Buckling states of adjacent molecules couple in a transverse field Ising type behavior. Based on the example of the metal organic framework topology MOF-5, we derived the phase diagram under applied strain, showing a normal phase, a parabuckling phase, and a ferrobuckling phase. At zero temperature, quantum phase transitions between the three phases can be induced by strain. This novel type of order opens a new path toward strain induced quantum phases.

Stabilization of Sr3Al2O6 Growth Templates for Ex Situ Synthesis of Freestanding Crystalline Oxide Membranes

A new synthetic approach has recently been developed for the fabrication of freestanding crystalline perovskite oxide nanomembranes, which involves the epitaxial growth of a water-soluble sacrificial layer. By utilizing an ultrathin capping layer of SrTiO₃, here we show that this sacrificial layer, as grown by pulsed laser deposition, can be stabilized in air and therefore be used as transferrable templates for ex situ epitaxial growth using other techniques. We find that the stability of these templates depends on the thickness of the capping layer. On these templates, freestanding superconducting SrTiO₃ membranes were synthesized ex situ using molecular beam epitaxy, enabled by the lower growth temperature which preserves the sacrificial layer. This study paves the way for the synthesis of an expanded selection of freestanding oxide membranes and heterostructures with a wide variety of ex situ growth techniques.

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.

From SrTiO3 to Cuprates and Back to SrTiO3: A Way Along Alex Müller’s Scientific Career

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.

Thermal magnetic fluctuations of a ferroelectric quantum critical point

Entanglement of two different quantum orders is of an interest of the modern condensed matter physics. One of the examples is the dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization. We investigate this effect at finite temperature and demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP). We calculate the magnetic susceptibility of a bulk sample on the paraelectric side of the FE QCP at finite temperature and find enhanced magnetic susceptibility near the FE QCP. We propose quantum paraelectric strontium titanate as a candidate material to search for dynamic multiferroicity. We estimate the magnitude of the magnetic susceptibility for this material and find that it is detectable experimentally.

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.

Large Polarons as Key Quasiparticles in SrTiO_{3} and SrTiO_{3}-Based Heterostructures

Despite its simple structure and low degree of electronic correlation, SrTiO_{3} (STO) features collective phenomena linked to charge transport and, ultimately, superconductivity, that are not yet fully explained. Thus, a better insight into the nature of the quasiparticles shaping the electronic and conduction properties of STO is needed. We studied the low-energy excitations of bulk STO and of the LaAlO_{3}/SrTiO_{3} two-dimensional electron gas (2DEG) by Ti L_{3} edge resonant inelastic x-ray scattering. In all samples, we find the hallmark of polarons in the form of intense dd+phonon excitations, and a decrease of the LO3-mode electron-phonon coupling when going from insulating to highly conducting STO single crystals and heterostructures. Both results are attributed to the dynamic screening of the large polaron self-induced polarization, showing that the low-temperature physics of STO and STO-based 2DEGs is dominated by large polaron quasiparticles.

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}.

A Lattice Litany for Transition Metal Oxides

In this tribute to K Alex Müller, I describe how his early insights have influenced future decades of research on perovskite ferroelectrics and more broadly transition metal oxides (TMOs) and related quantum materials. I use his influence on my own research journey to discuss impacts in three areas: structural phase transitions, precursor structure, and quantum paraelectricity. I emphasize materials functionality in ground, metastable, and excited states arising from competitions among lattice, charge, and spin degrees of freedom, which results in highly tunable landscapes and complex networks of multiscale configurations controlling macroscopic functions. I discuss competitions between short- and long-range forces as particularly important in TMOs (and related materials classes) because of their localized and directional metal orbitals and the polarizable oxygen ions. I emphasize crucial consequences of elasticity and metal–oxygen charge transfer.

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.

Unconventional Co-Existence of Insulating Nano-Regions and Conducting Filaments in Reduced SrTiO3: Mode Softening, Local Piezoelectricity, and Metallicity

Doped SrTiO3 becomes a metal at extremely low doping concentrations n and is even superconducting at n < 1020 cm−3, with the superconducting transition temperature adopting a dome-like shape with increasing carrier concentration. In this paper it is shown within the polarizability model and from first principles calculations that up to a well-defined carrier concentration nc transverse optic mode softening takes place together with polar nano-domain formation, which provides evidence of inhomogeneity and a two-component type behavior with metallicity coexisting with polarity. Beyond this region, a conventional metal is formed where superconductivity as well as mode softening is absent. For n ≤ nc the effective electron-phonon coupling follows the superconducting transition temperature. Effusion measurements, as well as macroscopic and nanoscopic conductivity measurements, indicate that the distribution of oxygen vacancies is local and inhomogeneous, from which it is concluded that metallicity stems from filaments which are embedded in a polar matrix as long as n ≤ nc.

Modified transverse Ising model for the dielectric properties of SrTiO3 films and interfaces

The transverse Ising model (TIM), with pseudospins representing the lattice polarization, is often used as a simple description of ferroelectric materials. However, we demonstrate that the TIM, as it is usually formulated, provides an incorrect description of SrTiO₃ films and interfaces because of its inadequate treatment of spatial inhomogeneity. We correct this deficiency by adding a pseudospin anisotropy to the model. We demonstrate the physical need for this term by comparison of the TIM to a typical Landau-Ginzburg-Devonshire model. We then demonstrate the physical consequences of the modification for two model systems: a ferroelectric thin film, and a metallic LaAlO₃/SrTiO₃ interface. We show that, in both cases, the modified TIM has a substantially different polarization profile than the conventional TIM. In particular, at low temperatures the formation of quantized states at LaAlO₃/SrTiO₃ interfaces only occurs in the modified TIM.

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.

Universal superconducting precursor in three classes of unconventional superconductors

A pivotal challenge posed by unconventional superconductors is to unravel how superconductivity emerges upon cooling from the generally complex normal state. Here, we use nonlinear magnetic response, a probe that is uniquely sensitive to the superconducting precursor, to uncover remarkable universal behaviour in three distinct classes of oxide superconductors: strontium titanate, strontium ruthenate, and the cuprate high-T_c materials. We find unusual exponential temperature dependence of the diamagnetic response above the transition temperature T_c, with a characteristic temperature scale that strongly varies with T_c. We correlate this scale with the sensitivity of T_c to local stress and show that it is influenced by intentionally-induced structural disorder. The universal behaviour is therefore caused by intrinsic, self-organized structural inhomogeneity, inherent to the oxides' perovskite-based structure. The prevalence of such inhomogeneity has far-reaching implications for the interpretation of electronic properties of perovskite-related oxides in general.

Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature T_{c} with the carrier density n predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasilocal. In contrast, we show that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic T_{c}(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity.

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.

Dynamic Multiferroicity of a Ferroelectric Quantum Critical Point

Quantum matter hosts a large variety of phases, some coexisting, some competing; when two or more orders occur together, they are often entangled and cannot be separated. Dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization, is an example where the two orders are impossible to disentangle. Here we demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP), since magnetic fluctuations are entangled with ferroelectric fluctuations. We thus suggest that any ferroelectric quantum critical point is an inherent multiferroic quantum critical point. We calculate the magnetic susceptibility near the FE QCP and find a region with enhanced magnetic signatures near the FE QCP and controlled by the tuning parameter of the ferroelectric phase. The effect is small but observable-we propose quantum paraelectric strontium titanate as a candidate material where the magnitude of the induced magnetic moments can be ∼5×10^{-7}  μ_{B} per unit cell near the FE QCP.

Evidence of Incoherent Carriers Associated with Resonant Impurity Levels and Their Influence on Superconductivity in the Anomalous Superconductor Pb_{1-x}Tl_{x}Te

We present a combined experimental and theoretical study of the evolution of the Fermi surface of the anomalous superconductor Pb_{1-x}Tl_{x}Te as a function of thallium concentration, drawing on a combination of magnetotransport measurements (Shubnikov-de Haas oscillations and the Hall coefficient), angle resolved photoemission spectroscopy, and density functional theory calculations of the electronic structure. Our results indicate that for Tl concentrations beyond a critical value, the Fermi energy coincides with resonant impurity states in Pb_{1-x}Tl_{x}Te, and we rule out the presence of an additional valence band maximum at the Fermi energy. A comparison to nonsuperconducting Pb_{1-x}Na_{x}Te implies that the presence of these impurity states at the Fermi energy provides the enhanced pairing interaction and thus also the anomalously high temperature superconductivity in this material.

Unconventional Multiband Superconductivity in Bulk SrTiO_{3} and LaAlO_{3}/SrTiO_{3} Interfaces

Although discovered many decades ago, superconductivity in doped SrTiO_{3} remains a topic of intense research. Recent experiments revealed that, upon increasing the carrier concentration, multiple bands cross the Fermi level, signaling the onset of Lifshitz transitions. Interestingly, T_{c} was observed to be suppressed across the Lifshitz transition of oxygen-deficient SrTiO_{3}; a similar behavior was also observed in gated LaAlO_{3}/SrTiO_{3} interfaces. Such a behavior is difficult to explain in the clean theory of two-band superconductivity, as the additional electronic states provided by the second band should enhance T_{c}. Here, we show that this unexpected behavior can be explained by the strong pair-breaking effect promoted by disorder, which takes place if the interband pairing interaction is subleading and repulsive. A consequence of this scenario is that, upon moving away from the Lifshitz transition, the two-band superconducting state changes from opposite-sign gaps to same-sign gaps.

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.

One-Dimensional Nature of Superconductivity at the LaAlO_{3}/SrTiO_{3} Interface

We examine superconductivity in LaAlO_{3}/SrTiO_{3} channels with widths that transition from the 1D to the 2D regime. The superconducting critical current is independent of the channel width and increases approximately linearly with the number of parallel channels. Signatures of electron pairing outside of the superconducting regime are also found to be independent of the channel width. Collectively, these results indicate that superconductivity exists at the boundary of these channels and is absent within the interior region of the channels. The intrinsic 1D nature of superconductivity at the LaAlO_{3}/SrTiO_{3} interface imposes strong physical constraints on possible electron pairing mechanisms.

Polaronic behavior in a weak-coupling superconductor

The nature of superconductivity in the dilute semiconductor SrTiO₃ has remained an open question for more than 50 y. The extremely low carrier densities ([Formula: see text]-[Formula: see text] cm^-3) at which superconductivity occurs suggest an unconventional origin of superconductivity outside of the adiabatic limit on which the Bardeen-Cooper-Schrieffer (BCS) and Migdal-Eliashberg (ME) theories are based. We take advantage of a newly developed method for engineering band alignments at oxide interfaces and access the electronic structure of Nb-doped SrTiO₃, using high-resolution tunneling spectroscopy. We observe strong coupling to the highest-energy longitudinal optic (LO) phonon branch and estimate the doping evolution of the dimensionless electron-phonon interaction strength ([Formula: see text]). Upon cooling below the superconducting transition temperature ([Formula: see text]), we observe a single superconducting gap corresponding to the weak-coupling limit of BCS theory, indicating an order of magnitude smaller coupling ([Formula: see text]). These results suggest that despite the strong normal state interaction with electrons, the highest LO phonon does not provide a dominant contribution to pairing. They further demonstrate that SrTiO₃ is an ideal system to probe superconductivity over a wide range of carrier density, adiabatic parameter, and electron-phonon coupling strength.

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.

Competition between electron pairing and phase coherence in superconducting interfaces

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin-orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high-energy dxz/dyz bands in the quantum well, more apt to host superconductivity.

Superconductivity at the Polar-Nonpolar Phase Boundary of SnP with an Unusual Valence State

Structural, magnetic, and electrical characterizations reveal that SnP with an unusual valence state (nominally Sn^{3+}) undergoes a ferroelectriclike structural transition from a simple NaCl-type structure to a polar tetragonal structure at approximately 250 K at ambient pressure. First-principles calculations indicate that the experimentally observed tetragonal distortion enhances the charge transfer from Sn to P, thereby making the polar tetragonal phase energetically more stable than the nonpolar cubic phase. Hydrostatic pressure is found to promptly suppress the structural phase transition in SnP, leading to the emergence of bulk superconductivity in a phase-competitive manner. These findings suggest that control of ferroelectriclike instability in a metal can be a promising way for creating novel superconductors.

Angle-resolved photoemission spectroscopy studies of metallic surface and interface states of oxide insulators

Over the last decade, conducting states embedded in insulating transition metal oxides (TMOs) have served as gateways to discovering and probing surprising phenomena that can emerge in complex oxides, while also opening opportunities for engineering advanced devices. These states are commonly realized at thin film interfaces, such as the well-known case of LaAlO3 (LAO) grown on SrTiO3 (STO). In recent years, the use of angle-resolved photoemission spectroscopy (ARPES) to investigate the k-space electronic structure of such materials led to the discovery that metallic states can also be formed on the bare surfaces of certain TMOs. In this topical review, we report on recent studies of low-dimensional metallic states confined at insulating oxide surfaces and interfaces as seen from the perspective of ARPES, which provides a direct view of the occupied band structure. While offering a fairly broad survey of progress in the field, we draw particular attention to STO, whose surface is so far the best-studied, and whose electronic structure is probably of the most immediate interest, given the ubiquitous use of STO substrates as the basis for conducting oxide interfaces. The ARPES studies provide crucial insights into the electronic band structure, orbital character, dimensionality/confinement, spin structure, and collective excitations in STO surfaces and related oxide surface/interface systems. The obtained knowledge increases our understanding of these complex materials and gives new perspectives on how to manipulate their properties.

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.

Isotope effect in superconducting n-doped SrTiO3

We report the influence on the superconducting critical temperature Tc in doped SrTiO3 of the substitution of the natural 16O atoms by the heavier isotope 18O. We observe that for a wide range of doping this substitution causes a strong (~50%) enhancement of Tc. Also the magnetic critical field Hc2 is increased by a factor ~2. Such a strong impact on Tc and Hc2, with a sign opposite to conventional superconductors, is unprecedented. The observed effect could be the consequence of strong coupling of the doped electrons to lattice vibrations (phonons), a notion which finds support in numerous optical and photo-emission studies. The unusually large size of the observed isotope effect supports a recent model for superconductivity in these materials based on strong coupling to the ferroelectric soft modes of SrTiO3.