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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Thermodynamic Theory of Proximity Ferroelectricity

Proximity ferroelectricity has recently been reported as a new design paradigm for inducing ferroelectricity, where a nonferroelectric polar material becomes a ferroelectric one by interfacing with a thin ferroelectric layer. Strongly polar materials, such as AlN and ZnO, which were previously unswitchable with an external field below their dielectric breakdown fields, can now be switched with practical coercive fields when they are in intimate proximity to a switchable ferroelectric. Here, we develop a general Landau-Ginzburg theory of proximity ferroelectricity in multilayers of nonferroelectrics and ferroelectrics to analyze their switchability and coercive fields. The theory predicts regimes of both “proximity switching,” where the multilayers collectively switch, and “proximity suppression,” where they collectively do not switch. The mechanism of the proximity ferroelectricity is an internal electric field determined by the polarization of the layers and their relative thickness in a self-consistent manner that renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier. Further reduction in the coercive field emerges from charged defects in the bulk that act as nucleation centers. The application of the theory to proximity ferroelectricity in Al x−1⁢ Sc x ⁢N/AlN and Zn 1−x ⁢Mg x ⁢O/ZnO bilayers is demonstrated. The theory further predicts that dielectric-ferroelectric and paraelectric-ferroelectric multilayers can potentially lead to induced ferroelectricity in the dielectric or paraelectric layers, resulting in the entire stack being switched, an exciting avenue for new discoveries. This thawing of “frozen ferroelectrics,” paraelectrics, and potentially dielectrics with high dielectric constants promises a large class of new ferroelectrics with exciting prospects for previously unrealizable domain-patterned optoelectronic and memory technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Proximity ferroelectricity in wurtzite heterostructures

Proximity ferroelectricity is an interface-associated phenomenon in electric-field-driven polarization reversal in a non-ferroelectric polar material induced by one or more adjacent ferroelectric materials. Here, in this paper, we report proximity ferroelectricity in wurtzite ferroelectric heterostructures. In the present case, the non-ferroelectric layers are AlN and ZnO, whereas the ferroelectric layers are Al 1−x B x N, Al 1−x Sc x N and Zn 1−x Mg x O. The layered structures include nitride–nitride, oxide–oxide and nitride–oxide stacks that feature two-layer (asymmetric) and three-layer (symmetric) configurations. Ferroelectric switching in both layers is validated by multimodal characterization methods, including polarization hysteresis, anisotropic chemical etching, second harmonic generation, piezo response force microscopy, electromechanical testing and atomic resolution polarization orientation imaging in real space by scanning transmission electron microscopy. We present a physical switching model in which antipolar nuclei originate in the ferroelectric layer and propagate towards the internal non-ferroelectric interface. The domain wall leading edge produces elastic and electric fields that extend beyond the interface at close proximity, reducing the switching barrier in the non-ferroelectric layer, and allowing complete domain propagation without breakdown. Density functional theory calculations of polymorph energies, reversal barriers and domain wall energies support this model. Proximity ferroelectricity enables polarization reversal in wurtzites without the chemical or structural disorder that accompanies elemental substitution, opening new questions and opportunities regarding interface-based ferroelectricity.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Proximity Ferroelectricity in Compositionally Graded Structures

Proximity ferroelectricity is a novel paradigm for inducing ferroelectricity in a non-ferroelectric polar material, such as AlN or ZnO that are typically unswitchable with an external field below their dielectric breakdown field. When placed in direct contact with a thin switchable ferroelectric layer (such as Al 1-x Sc x N or Zn 1-x Mg x O), they become a practically switchable ferroelectric. Using the thermodynamic Landau-Ginzburg-Devonshire theory, in this work, we perform the finite element modeling of the polarization switching in the compositionally graded AlN-Al 1-x Sc x N, ZnO-Zn 1-x Mg x O, and MgO-Zn 1-x Mg x O structures sandwiched in both a parallel-plate capacitor geometry as well as in a sharp probe-planar electrode geometry. We reveal that the compositionally graded structure allows the simultaneous switching of spontaneous polarization in the whole system by a coercive field significantly lower than the electric breakdown field of unswitchable polar materials. The physical mechanism is the depolarization electric field determined by the gradient of chemical composition “x”. The field lowers the steepness of the switching barrier in the otherwise unswitchable parts of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures. In the MgO-like regions of the compositionally graded MgO-Zn 1-x Mg x O structure, a shallow double-well free energy potential emerges. Proximity ferroelectric switching of the compositionally graded structures placed in the probe-electrode geometry occurs due to nanodomain formation under the tip. We predict that a gradient of chemical composition “x” significantly lowers effective coercive fields of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures compared to the coercive fields of the corresponding multilayers with a uniform chemical composition in each layer. A tip-induced switching further lowers the coercive field, enabling control of ferroelectric domains in otherwise unswitchable compositionally graded structures, which can provide nanoscale domain control for memory, actuation, sensing, and optical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tip-based proximity ferroelectric switching and piezoelectric response in wurtzite multilayers

Proximity ferroelectricity is a paradigm for inducing ferroelectricity when a nonferroelectric polar material (such as Al⁢ N), which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer (such as Al 1−𝑥 ⁢Sc 𝑥 ⁢N). Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite-element modeling, we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the Al 1−𝑥 ⁢Sc 𝑥 ⁢N/Al⁢ N bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of “proximity switching” (when all layers collectively switch) and the regime of “proximity suppression” (when they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezoresponse and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as Al⁢ N), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the “otherwise unswitchable” polar layers. Tip-based control of domains in otherwise nonferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing, and optical applications. The ability of the tip-induced proximity switching to differentially switch multilayers, based on the order of the layers, provides a powerful tool for selective domain engineering.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Abstract Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe 2 . The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe 2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

42 ENGINEERING↗
DOE OSTI2026

Embedded Ferroelectric Nanoclusters can drive Polarization Reversal in a Non-Ferroelectric Polar Film via the Proximity Effect

Heterogeneous nucleation from defects dominates the electric field required for polarization switching of ferroelectrics. Here, we consider the switching of a nominally non-switchable polar thin film of AlN due to the proximity effect arising from embedded ferroelectric nanoclusters of Al 1-x Sc x N. Using a Landau-Ginzburg-Devonshire thermodynamic approach and finite element modeling, we study the influence of nanocluster shape on polarization switching and domain nucleation emerging in AlN. The ferroelectric nanocluster boundary is modeled as a thin layer transitioning from Al 1-x Sc x N to AlN. We analyze the conditions under which polarization switching in the AlN film occurs at coercive fields significantly lower than its dielectric breakdown field. In the presence of spike-like Al 1-x Sc x N nanoclusters, the proximity effect enables switching of the spontaneous polarization in AlN and significantly reduces the corresponding coercive field. The internal field, which is depolarizing inside the AlN (due to its larger spontaneous polarization) and polarizing within the ferroelectric Al 1-x Sc x N nanoclusters (due to its smaller spontaneous polarization), lowers the potential barrier in the clusters and nucleates nanodomains at the Al 1-x Sc x N-AlN interface, forming localized regions of reversed polarization. Proximity effect can thus provide a pathway towards "thawing" previously "frozen" ferroelectrics through engineered nucleation for memory, actuation and optical technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

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

Here, 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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Ferroelectric Semimetals with α-Bi/SnSe van der Waals Heterostructures and Their Topological Currents

We show that proximity effects can be utilized to engineer van der Waals heterostructures (vdWHs) displaying semimetallic spin-ferroelectricity locking, where ferroelectricity and semimetallic spin states are confined to different layers, but are correlated by means of proximity effects. Our findings are supported by first principles calculations involving α-Bi/SnSe bilayers. We show that such systems support ferroelectrically switchable nonlinear anomalous Hall effect originating from large Berry curvature dipoles as well as direct and inverse spin Hall effects with giant bulk spin-charge interconversion efficiencies. In conclusion, the giant efficiencies are consequences of the proximity-induced semimetallic nature of low energy electron states, which are shown to behave as two-dimensional pseudo-Weyl fermions by means of symmetry analysis and first principles calculations as well as direct angle-resolved photoemission spectroscopy measurements.

2-dimensional systems↗
DOE OSTI2021

Two-dimensional multifunctional materials from endohedral fullerenes

A multifunctional two-dimensional (2D) material is theoretically predicted based on systematic ab initio calculations and model simulations for the honeycomb lattice of endohedral fullerene W@C 28 molecules. It has structural bistability, ferroelectricity, multiple magnetic phases, and excellent valley characters and can be easily functionalized by the proximity effect with magnetic isolators such as MnTiO 3 . Furthermore, we may also manipulate the valley Hall and spin transport properties by selectively switching a few W@C 28 molecules to the metastable phase. These conclusions contribute to integrating different functions in a single 2D material for technological innovations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Enhanced pyroelectric properties of Bi 1-x La x FeO 3 thin films

There is growing interest in the study of thin-film pyroelectric materials because of their potential for high performance thermal-energy conversion, thermal sensing, and beyond. Electrothermal susceptibilities, such as pyroelectricity, are known to be enhanced in proximity to polar instabilities, and this is conventionally accomplished by positioning the material close to a temperature-driven ferroelectric-to-paraelectric phase transition. The high Curie temperature (T C ) for many ferroelectrics, however, limits the utility of these materials at room-temperature. Here, the nature of pyroelectric response in thin films of the widely studied multiferroic Bi 1-x La x FeO 3 (x = 0-0.45) is probed. While BiFeO 3 itself has a high T C , lanthanum substitution results in a chemically induced lowering of the ferroelectric-to-paraelectric and structural-phase transition. The effect of isovalent lanthanum substitution on the structural, dielectric, ferroelectric, and pyroelectric response is investigated using reciprocal-space-mapping studies; field-, frequency-, and temperature-dependent electrical measurements; and phase-sensitive pyroelectric measurements, respectively. While BiFeO 3 itself has a rather small pyroelectric coefficient at room temperature (~-40 μC/m 2 K), 15% lanthanum substitution results in an enhancement of the pyroelectric coefficient by 100% which is found to arise from a systematic lowering of T C .

36 MATERIALS SCIENCE↗
DOE OSTI2023

One Dimensional Topological Nanomaterials and Superconductivity (Final Technical Report)

The project synthesized and made transport properties of topological crystalline insulator tin telluride (SnTe) nanowires and other topological materials, such as MoTe 2 and WTe 2 . The transport properties of the nanowires were correlated with the diameter of the nanowire, in terms of the ferroelectric phase transition temperature, magnetoresistance response, and Josephson junction behaviors as a function of the nanowire diameter. The most important observation was the proximity-induced superconductivity in SnTe nanowires, which suggests time reversal symmetry breaking.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Temperature-independent giant dielectric response in transitional BaTiO 3 thin films

Ferroelectric materials exhibit the largest dielectric permittivities and piezoelectric responses in nature, making them invaluable in applications from supercapacitors or sensors to actuators or electromechanical transducers. The origin of this behavior is their proximity to phase transitions. However, the largest possible responses are most often not utilized due to the impracticality of using temperature as a control parameter and to operate at phase transitions. This has motivated the design of solid solutions with morphotropic phase boundaries between different polar phases that are tuned by composition and that are weakly dependent on temperature. Thus far, the best piezoelectrics have been achieved in materials with intermediate (bridging or adaptive) phases. But so far, complex chemistry or an intricate microstructure has been required to achieve temperature-independent phase-transition boundaries. Here, we report such a temperature-independent bridging state in thin films of chemically simple BaTiO3. A coexistence among tetragonal, orthorhombic, and their bridging low-symmetry phases are shown to induce continuous vertical polarization rotation, which recreates a smear in-transition state and leads to a giant temperature-independent dielectric response. The current material contains a ferroelectric state that is distinct from those at morphotropic phase boundaries and cannot be considered as ferroelectric crystals. We believe that other materials can be engineered in a similar way to contain a ferroelectric state with gradual change of structure, forming a class of transitional ferroelectrics. Similar mechanisms could be utilized in other materials to design low-power ferroelectrics, piezoelectrics, dielectrics, or shape-memory alloys, as well as efficient electro- and magnetocalorics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Antiphase-Boundary-Engineered Domain Switching in a (110)-Oriented BiFeO 3 Film

A ferroelectric domain wall memory device exploits the presence (or absence) of domain walls as the basis for information storage. Although structural defects strongly influence ferroelectric domain wall nucleation and growth, this correlation is far from being fully understood. For example, a single defect can play opposing roles: it can act as a nucleation site to initiate domain switching or, conversely, serve as a pinning center inhibiting domain wall motion. This is particularly the case for antiphase boundaries (APBs), whose influence on switching remains relatively unexplored despite being ubiquitous in oxide perovskite ferroelectrics. Here, we use aberration-corrected scanning transmission microscopy and in situ transmission electron microscopy under an applied bias to extensively characterize the influence of an APB on the switching behavior in a (110)-oriented BiFeO 3 thin film. We demonstrate that deterministic nucleation occurs in the proximity of a vertically oriented APB, following which domain growth occurs laterally in a symmetric fashion. Atomic-scale structural analysis reveals that the shear operation vector for the APB is 1/2[110]; this half-unit-cell shift extends over a few nanometers, implying that the APB plane is inclined toward the imaging direction. The symmetric switching observation is attributed to local inhomogeneous lattice strain and a reduction of polarization caused by the APB. These results demonstrate that an extended structural defect can be used as an active switching element rather than a stumbling block in reprogrammable domain-wall-based devices. Ultimately, this will expand the capabilities of ferroelectric thin films for future electronic devices based on ferroelectric domain walls.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Propagation of priors for more accurate and efficient spectroscopic functional fits and their application to ferroelectric hysteresis

Multi-dimensional spectral-imaging is a mainstay of the scanning probe and electron microscopies, micro-Raman, and various forms of chemical imaging. In many cases, individual spectra can be fit to a specific functional form, with the model parameter maps, providing direct insight into material properties. Since spectra are often acquired across a spatial grid of points, spatially adjacent spectra are likely to be similar to one another; yet, this fact is almost never used when considering parameter estimation for functional fits. On datasets tried here, we show that by utilizing proximal information, whether it be in the spatial or spectral domains, it is possible to improve the reliability and increase the speed of such functional fits by ~2-3x, as compared to random priors. We explore and compare three distinct new methods: (1) spatially averaging neighborhood spectra, and propagating priors based on functional fits to the averaged case, (2) hierarchical clustering-based methods where spectra are grouped hierarchically based on response, with the priors propagated progressively down the hierarchy, and (3) regular clustering without hierarchical methods with priors propagated from fits to cluster means. Our results highlight that utilizing spatial and spectral neighborhood information is often critical for accurate parameter estimation in noisy environments, which we show for ferroelectric hysteresis loops acquired on a prototypical PbTiO3 thin film with piezoresponse spectroscopy. This method is general and applicable to any spatially measured spectra where functional forms are available. Examples include exploring the superconducting gap with tunneling spectroscopy, using the Dynes formula, or current-voltage curve fits in conductive atomic force microscopy mapping. Here we explore the problem for ferroelectric hysteresis, which, given its large parameter space, constitutes a more difficult task than, for example, fitting current-voltage curves with a Schottky emission formula.

42 ENGINEERING↗
DOE OSTI2023

Domain wall motion across microstructural features in polycrystalline ferroelectric films

This paper describes the effect of microstructural features such as grain boundaries and triple points on the pinning of domain wall motion in perovskite Pb(Zr 0.52 Ti 0.48 )O 3 (PZT) films on polycrystalline SrRuO 3 /SrTiO 3 substrates. Here, spatial variability in the collective domain wall dynamics was assessed using non-linearity mapping via Band Excitation Piezoresponse Force Microscopy (BE-PFM). Collocating the non-linearity maps with triple point locations (as visualized by EBSD) allowed for exploration of the effects that local microstructure (e.g., grain boundary) have on domain wall motion. It was found that the extrinsic behavior varied with both the misorientation angle and the proximity to the grain boundary. The width of influence of individual grain boundaries on the motion of domain walls was a function of the character of the grain boundary; random grain boundaries exhibit deeper minima in α d /d 33,initial and larger widths of influence (up to 905 nm) compared to coincident site lattice (CSL) boundaries (up to 572 nm). Additionally, triple points containing larger numbers of random boundaries exhibited non-Rayleigh behavior to greater distances, suggesting that the triple point provides either a deep potential minimum or a region where domain wall motion is unfavorable.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Josephson detection of time-reversal symmetry broken superconductivity in SnTe nanowires

A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. In this work, we present such a case: we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in JJs and observe a deviation from the standard CPR. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. The analysis examines how multiband effects and the experimentally visualized ferroelectric domain walls give rise to this behavior, giving insight into the Josephson effect in materials that possess ferroelectricity and/or multiband superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

High temperature sensor/microphone development for active noise control

The industrial and scientific communities have shown genuine interest in electronic systems which can operate at high temperatures, among which are sensors to monitor noise, vibration, and acoustic emissions. Acoustic sensing can be accomplished by a wide variety of commercially available devices, including: simple piezoelectric sensors, accelerometers, strain gauges, proximity sensors, and fiber optics. Of the several sensing mechanisms investigated, piezoelectrics were found to be the most prevalent, because of their simplicity of design and application and, because of their high sensitivity over broad ranges of frequencies and temperature. Numerous piezoelectric materials are used in acoustic sensors today; but maximum use temperatures are imposed by their transition temperatures (T(sub c)) and by their resistivity. Lithium niobate, in single crystal form, has the highest operating temperature of any commercially available material, 650 C; but that is not high enough for future requirements. Only two piezoelectric materials show potential for use at 1000 C; AlN thin film reported to be piezoactive at 1150 C, and perovskite layer structure (PLS) materials, which possess among the highest T(sub c) (greater than 1500 C) reported for ferroelectrics. A ceramic PLS composition was chosen. The solid solution composition, 80% strontium niobate (SN) and 20% strontium tantalate (STa), with a T(sub c) approximately 1160 C, was hot forged, a process which concurrently sinters and renders the plate-like grains into a highly oriented configuration to enhance piezo properties. Poled samples of this composition showed coupling (k33) approximately 6 and piezoelectric strain constant (d33) approximately 3. Piezoactivity was seen at 1125 C, the highest temperature measurement reported for a ferroelectric ceramic. The high temperature piezoelectric responses of this, and similar PLS materials, opens the possibility of their use in electronic devices operating at temperatures up to 1000 C. Concurrent with the materials study was an effort to define issues involved in the development of a microphone capable of operation at temperatures up to 1000 C; important since microphones capable of operation above 260 C are not generally available. The distinguishing feature of a microphone is its diaphragm which receives sound from the atmosphere: whereas, most other acoustic sensors receive sound through the solid structure on which they are installed. In order to gain an understanding of the potential problems involved in designing and testing a high temperature microphone, a prototype was constructed using a commercially available lithium niobate piezoelectric element in a stainless steel structure. The prototype showed excellent frequency response at room temperature, and responded to acoustic stimulation at 670 C, above which temperature the voltage output rapidly diminished because of decreased resistivity in the element. Samples of the PLS material were also evaluated in a simulated microphone configuration, but their voltage output was found to be a few mV compared to the 10 output of the prototype.

Shrout, Thomas R.↗
DOE OSTI2020

Superconductivity in dilute SrTiO 3 : A review

Doped SrTiO 3 , one of the most dilute bulk systems to display superconductivity, is perhaps the first example of an unconventional superconductor, as it does not fit into the standard BCS paradigm. More than five decades of research has revealed a rich temperature-carrier concentration phase diagram that showcases a superconducting dome, proximity to a putative quantum critical point, Lifshitz transitions, a multi-gap pairing state and unusual normal-state transport properties. Research has also extended beyond bulk SrTiO 3 , ushering the new field of SrTiO 3 -based heterostructures. Because many of these themes are also featured in other quantum materials of contemporary interest, recent years have seen renewed interest in SrTiO 3 . Here, we review the challenges and recent progress in elucidating the superconducting state of this model system. At the same time that its extreme dilution requires to revisit several of the approximations that constitute the successful Migdal–Eliashberg description of electron–phonon superconductivity, including the suppression of the Coulomb repulsion via the Tolmachev–Anderson–Morel mechanism, it opens interesting routes for alternative pairing mechanisms whose applicability remains under debate. For instance, pairing mechanisms involving longitudinal optical phonons have to overcome the hurdles created by the anti-adiabatic nature of the pairing interaction, whereas mechanisms that rely on the soft transverse optical phonons associated with incipient ferroelectricity face challenges related to the nature of the electron–phonon coupling. Proposals in which pairing is mediated by plasmons or promoted locally by defects are also discussed. In conclusion, we finish by surveying the existing evidence for multi-band superconductivity and outlining promising directions that can potentially shed new light on the rich problem of superconductivity in SrTiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗