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Results for “suppressed phase transitions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Anisotropic magnetism of polymorphic ErAl 3

ErAl 3 can form in either a trigonal (α) or cubic (β) polymorph and this paper investigates the physical properties of these polymorphs through characterizations of single crystals grown in an aluminum flux. Here, we demonstrate that polymorph selection can be achieved based on the nominal composition of the crystal growth. Magnetic measurements confirm that both β-ErAl 3 and α-ErAl 3 order antiferromagnetically at low temperatures. β-ErAl 3 undergoes antiferromagnetic ordering at a Néel temperature T N = 5.1 K, and the transition is suppressed continually with applied field. α-ErAl 3 displays more complex behavior, with successive magnetic transitions at T N = 5.7 K and T 2 = 4.6 K for zero field, where heat capacity and dilatometry measurements evidence that these transitions are second and first order, respectively. Under magnetic field, strong anisotropy is revealed in α-ErAl 3 , with several steplike metamagnetic transitions observed below T 2 for H ∥ c. These transitions produce sequential magnetization plateaus near one-half of the apparent saturation magnetization. The electrical resistivity of α-ErAl 3 is strongly coupled to its magnetism. At T = 2 K, we observe a positive magnetoresistance reaching 60%, with distinct anomalies at the metamagnetic transitions. The results are summarized in H-T phase diagrams that demonstrate complex magnetic behavior for α-ErAl 3 , suggesting an important role of competing interactions in this metallic system that possesses characteristics of Ising physics.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Abedian, B.↗
DOE OSTI2021

Estimation of secondary organic aerosol viscosity from explicit modeling of gas-phase oxidation of isoprene and α -pinene

Abstract. Secondary organic aerosols (SOA) are major components of atmospheric fine particulate matter, affecting climate and air quality. Mounting evidence exists that SOA can adopt glassy and viscous semisolid states, impacting formation and partitioning of SOA. In this study, we apply the GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere) model to conduct explicit chemical modeling of isoprene photooxidation and α-pinene ozonolysis and their subsequent SOA formation. The detailed gas-phase chemical schemes from GECKO-A are implemented into a box model and coupled to our recently developed glass transition temperature parameterizations, allowing us to predict SOA viscosity. The effects of chemical composition, relative humidity, mass loadings and mass accommodation on particle viscosity are investigated in comparison with measurements of SOA viscosity. The simulated viscosity of isoprene SOA agrees well with viscosity measurements as a function of relative humidity, while the model underestimates viscosity of α-pinene SOA by a few orders of magnitude. This difference may be due to missing processes in the model, including autoxidation and particle-phase reactions, leading to the formation of high-molar-mass compounds that would increase particle viscosity. Additional simulations imply that kinetic limitations of bulk diffusion and reduction in mass accommodation coefficient may play a role in enhancing particle viscosity by suppressing condensation of semi-volatile compounds. The developed model is a useful tool for analysis and investigation of the interplay among gas-phase reactions, particle chemical composition and SOA phase state.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Structural evolution during solution-based synthesis of Li 7 P 3 S 11 solid electrolyte by synchrotron X-ray total scattering

Solution-based synthesis has emerged as a promising approach for scalable and efficient synthesis of solid electrolytes (SEs). However, the ionic conductivity of solution-synthesized SEs is much lower than that of SEs synthesized by solid state approaches. The structural evolution during the synthesis of SEs is crucial to explaining the decreased ionic conductivities but has not been well understood. Here, in this work, we use synchrotron X-ray total scattering combined with pair distribution function (PDF) analysis to understand the structural evolution during annealing of the solution-processed precursor for the synthesis of Li 7 P 3 S 11 SEs. Combining Bragg diffraction and diffuse scattering, X-ray total scattering enables detection of structural information including phase transition and crystallinity. The results show that the formation of Li 7 P 3 S 11 glass-ceramic starts at 230 °C. Increasing the annealing temperature helps to improve the crystallinity, but the degree of crystallization is still lower than 70.3% even after annealing at 290 °C when thermal decomposition of Li 7 P 3 S 11 to Li 4 P 2 S 6 has occurred. PDF analysis also revealed the existence of acetonitrile used in the solution-based synthesis in the SEs after annealing at high temperatures. The results rationalize the synthesis–property relationship, explain why annealing at 290 °C provides the highest ionic conductivity at the studied temperatures due to an optimal balance for achieving a high crystallinity while suppressing severe decomposition of Li 7 P 3 S 11 , and provide novel insights to develop approaches for synthesizing superior Li 7 P 3 S 11 SEs on a large scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Pressure effect on magnetism and valence in ferromagnetic superconductor Eu(Fe 0.75 Ru 0.25 ) 2 As 2

Eu(Fe 0.75 Ru 0.25 ) 2 As 2 is an intriguing system with unusual coexistence of superconductivity and ferromagnetism, providing a unique platform to study the nature of such coexistence. To establish a magnetic phase diagram, time-domain synchrotron Mössbauer experiments in 151 Eu have been performed on a single crystalline Eu(Fe 0.75 Ru 0.25 ) 2 As 2 sample under hydrostatic pressures and at low temperatures. Upon compression the magnetic ordering temperature increases sharply from 20 K at ambient pressure, reaching ~49 K at 10.1GPa. With further compression, the magnetic order is suppressed and eventually collapses. Isomer shift values from Mössbauer measurements and x-ray absorption spectroscopy data at Eu L 3 edge show that pressure drives Eu ions to a homogeneous intermediate valence state with mean valence of ~2.4 at 27.4 GPa, possibly responsible for the suppression of magnetism. Synchrotron powder x-ray diffraction experiment reveals a tetragonal to collapsed-tetragonal structural transition around 5 GPa, a lower transition pressure than in the parent compound. Furthermore, these results provide guidance to further work investigating the interplay of superconductivity and magnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Polytype selection in the antisolvent-free crystallization of formamidinium lead iodide using alkylammonium chlorides

This work presents a systematic study of how the size of the C 0 –C 4 alkylammonium chloride additive directs the crystallization pathway in antisolvent-free FAPbI 3 films. We find that larger cations promote the intermediate formation of hexagonal polytypes, correlating with enhanced film crystallinity. Understanding the nucleation, crystallization, and phase transition mechanisms in perovskite thin films produced without antisolvent quenching is crucial for improving phase stability and optoelectronic performance at scale. By means of in situ grazing incidence wide-angle X-ray scattering experiments, we show that the nature of alkylammonium chloride (RACl) additives significantly influences the crystallization dynamics and temperature-dependent stability of formamidinium lead iodide (FAPbI 3 ) perovskite films formed using antisolvent-free processes. The in situ experiments reveal that the effective radius of the RA + cation and the vapor pressure of the RA 0 conjugate base are critical factors affecting the crystallization pathway and film morphology. C 2 –C 3 additives with moderate chain lengths may strike a balance between promoting the early crystallization of the cubic 3C phase while suppressing unwanted phases. This balance promotes the formation of highly crystalline cubic perovskite phase with well-oriented structure and better optoelectronic properties. These findings provide guidance regarding the design of additives to crystallize more stable and efficient perovskite films for optoelectronic applications.

Marchezi, Paulo E↗
DOE OSTI2020

22 K superconductivity in Ba Fe 2 As 2 exposed to F 2

Several previous reports on undoped AEFe 2 As 2 (AE = alkaline earth metal) point to drops in resistivity indicative of possible superconductivity and some degree of Meissner effect in the magnetic susceptibility. Also, based on both resistivity and magnetic susceptibility measurements, controlled exposure to water vapor has been shown to induce superconductivity in AEFe 2 As 2 . In our study, BaFe 2 As 2 single crystals grown using the self-flux method showed a full resistive drop around 22 K and magnetic shielding, when exposed to fluorine gas postgrowth. Our measurements indicate electron (donor) doping via atomic substitution of F for As is concurrent with the observed superconductivity, which sheds light on the likely effect of exposure to water vapor in previous work. Like doping experiments (such as substitution of Co for Fe, P for As, or K for Ba) in AEFe 2 As 2 to date, the present work is consistent with suppression of the spin density wave transition coincident with the appearance of T c . In addition to answering the puzzle of superconductivity in undoped or water vapor exposed AEF 2 As 2 , our results also represent a fast (20 min exposure to 5% F in He) and reliable method suitable for inducing superconductivity in thin films of AEFe 2 As 2 . As a result, some supportive work on BaFe 2 As 2 exposed to Cl 2 is also presented.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Revealing the competition between charge density wave and superconductivity in CsV 3 Sb 5 through uniaxial strain

In this paper we report the effect of uniaxial strain ε applied along the crystalline a axis on the newly discovered kagome superconductor CsV 3 Sb 5 . At ambient conditions, CsV 3 Sb 5 shows a charge-density wave (CDW) transition at T CDW = 94.5K and superconducts below T c = 3.34K. In our paper, when the uniaxial strain ε is varied from –0.90% to 0.90%,T c monotonically increases by ~33% from 3.0 to 4.0 K, giving rise to the empirical relation T c (ε) = 3.4 + 0.56ε + 0.12ε 2 . On the other hand, for ε changing from –0.76% to 1.26%,TCDW decreases monotonically by ~10% from 97.5 to 87.5 K with T CDW (ε) = 94.5 – 4.72ε – 0.60ε 2 . The opposite response of T c and T CDW to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the c axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in Tc with decreasing c is caused primarily by the suppression of T CDW , rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of T CDW with respect to the changes in the c axis arises from the impact of the latter on the trilinear coupling between the $M$$^{+}_{1}$ and the $L$$^{–}_{2}$ phonon modes associated with the CDW. Altogether, our paper reveals that the c-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pairing and Pair Breaking by Gauge Fluctuations in Bilayer Composite Fermion Metals

We study interlayer pairing of composite fermions in the total $\nu=1/2+1/2$ quantum Hall bilayer as a possible framework for understanding the experimentally observed transition from a compressible state at large layer spacing to a bilayer quantum Hall state at small layer spacing. We consider a model in which the effective interlayer composite fermion pairing interaction mediated by the Chern-Simons gauge fields in the two layers is singular with both attractive (out-of-phase) and repulsive (in-phase) components diverging at low frequency. If only the more singular attractive interaction is included the pairing gap obtained by solving the gap equation is proportional to the inverse of the layer spacing squared. In the so-called local approximation, we find that when the less singular repulsive interactions are also included the pairing gap still falls off as inverse layer spacing squared, consistent with recent analyses, but is strongly suppressed to a degree that may account for the fact that this predicted inverse square dependence is not observed experimentally. The analytically obtained local approximation solutions are then used as a starting point to numerically iterate the full gap equation to assess the validity of the approximation in this limit.

Deng, Haoyun↗
NASA NTRS2001

Effects of Gravity on Cocurrent Two-Phase Gas-Liquid Flows Through Packed Columns

This work presents the experimental results of research on the influence of gravity on flow pattern transitions, pressure drop and flow characteristics for cocurrent gas-liquid two-phase flow through packed columns. The flow pattern transition data indicates that the pulse flow regime exists over a wider range of gas and liquid flow rates under reduced gravity conditions compared to normal gravity cocurrent down-flow. This is illustrated by comparing the flow regime transitions found in reduced gravity with the transitions predicted by Talmor. Next, the effect of gravity on the total pressure drop in a packed column is shown to depend on the flow regime. The difference is roughly equivalent to the liquid static head for bubbly flow but begins to decrease at the onset of pulse flow. As the spray flow regime is approached by increasing the gas to liquid ratio, the effect of gravity on pressure drop becomes negligible. Finally, gravity tends to suppress the amplitude of each pressure pulse. An example of this phenomenon is presented.

Motil, Brian J.↗
DOE OSTI2025

Dynamic Competition between Hubbard and Superexchange Interactions Selectively Localizes Electrons and Holes through Polarons

Controlling the effects of photoexcited polarons in transition metal oxides can enable the long time-scale charge separation necessary for renewable energy applications and controlling new quantum phases through dynamically tunable electron–phonon coupling. In previously studied transition metal oxides, polaron formation is facilitated by a photoexcited ligand-to-metal charge transfer (LMCT). When the polaron is formed, oxygen atoms move away from iron centers, which increases carrier localization at the metal center and decreases charge hopping. Studies of yttrium iron garnet and erbium iron oxide have suggested that strong electron and spin correlations can modulate photoexcited polaron formation. To understand the interplay between strong spin and electronic correlations in highly polar materials, we studied gadolinium iron oxide (GdFeO 3 ), which selectively forms photoexcited polarons through an Fe–O–Fe superexchange interaction. Excitation-wavelength-dependent transient extreme ultraviolet (XUV) spectroscopy selectively excites LMCT and metal-to-metal charge transfer (MMCT) transitions. Here, the LMCT transition suppresses photoexcited polaron formation due to the balance between superexchange and Hubbard interactions, while MMCT transitions result in photoexcited polaron formation within 250 ± 40 fs. Ab initio theory demonstrates that electron and hole polarons localize on iron centers following MMCT. In addition to understanding how strong electronic and spin correlations can control strong electron–phonon coupling, these experiments separately measure electron and hole polaron interactions on neighboring metal centers for the first time, providing insight into a large range of charge-transfer and Mott–Hubbard insulators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

High-Energy Density Li-Ion Battery Cathode Using Only Industrial Elements

Li-ion batteries are crucial for the global energy transition to renewables; however, their scalability is limited by the supply of key elements used in commercial cathodes (e.g., Ni, Mn, Co, P). Therefore, there is an urgent need for next-generation cathodes composed of widely available and industrially scalable elements. Here, we introduce a Li-rich cathode based on the known material Li 2 FeS 2 , composed of low-cost elements (Al, Fe, S) that are globally mined and refined at an industrial scale. The substitution of redox-inactive Al 3+ for Fe 2+ achieves remarkably high degrees of anion redox, which, in turn, yields high gravimetric capacity (≈450 mAh·g –1 ) and energy density (≳1000 Wh·kg –1 ). We show that Al 3+ enables high degrees of delithiation by stabilizing the delithiated state, suppressing phase transformations that would otherwise prevent deep delithiation and extensive anion redox. This mechanistic insight offers new possibilities for developing scalable, next-generation Li-ion battery cathodes to meet pressing societal needs.

25 ENERGY STORAGE↗
DOE OSTI2021

Chemomechanically Stable Ultrahigh-Ni Single-Crystalline Cathodes with Improved Oxygen Retention and Delayed Phase Degradations

The pressing demand in electrical vehicle (EV) markets for high-energy-density lithium-ion batteries (LIBs) requires further increasing the Ni content in high-Ni and low-Co cathodes. However, the commercialization of high-Ni cathodes is hindered by their intrinsic chemomechanical instabilities and fast capacity fade. The emerging single-crystalline strategy offers a promising solution, yet the operation and degradation mechanism of single-crystalline cathodes remain elusive, especially in the extremely challenging ultrahigh-Ni (Ni > 90%) regime whereby the phase transformation, oxygen loss, and mechanical instability are exacerbated with increased Ni content. Herein, we decipher the atomic-scale stabilization mechanism controlling the enhanced cycling performance of an ultrahigh-Ni single-crystalline cathode. We find that the charge/discharge inhomogeneity, the intergranular cracking, and oxygen-loss-related phase degradations that are prominent in ultrahigh-Ni polycrystalline cathodes are considerably suppressed in their single-crystalline counterparts, leading to improved chemomechanical and cycling stabilities of the single-crystalline cathodes. Furthermore, our work offers important guidance for designing next-generation single-crystalline cathodes for high-capacity, long-life LIBs.

25 ENERGY STORAGE↗
DOE OSTI2025

Magnon damping and mode softening in quantum double-exchange ferromagnets

We present a comprehensive analysis of the magnetic excitations and electronic properties of fully quantum double-exchange ferromagnets, i.e. systems where ferromagnetic (FM) ordering emerges from the competition between spin, charge, and orbital degrees of freedom, but without the canonical approximation of using classical localized spins. Specifically, we investigate spin excitations within the Kondo lattice-like model, as well as a two-orbital Hubbard Hamiltonian in proximity to the orbital-selective Mott phase. Computational analysis of the magnon dispersion, damping, and spectral weight within these models reveals unexpected phenomena, such as magnon mode softening and the anomalous decoherence of magnetic excitations as observed in earlier experimental efforts, but explained here without the use of the phononic degrees of freedom. We show that these effects are intrinsically linked to incoherent spectral features near the Fermi level, which arise due to the quantum nature of the local (on-site) triplets. This incoherent spectrum leads to a Stoner-like continuum on which spin excitations scatter, governing magnon lifetime and strongly influencing the dynamical spin structure factor. Our study explores the transition from coherent to incoherent magnon spectra by varying the electron density. Furthermore, we demonstrate that the magnitude of the localized spin mitigates decoherence by suppressing the incoherent spectral contributions near the Fermi level. We also discuss the effective J 1 –J 2 spin Hamiltonian, which can accurately describe the large doping region characterized by the magnon-mode softening. Finally, we show that this behavior is also present in multiorbital models with partially filled orbitals, namely, in systems without localized spin moments, provided that the model is in a strong coupling regime. Our results potentially have far-reaching implications for understanding FM ordering in various multi-band systems. These findings establish a previously unknown direct connection between the electronic correlations of those materials and spin excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Probing intrinsic magnetization dynamics of the Y 3⁢ Fe 5 ⁢O 12 /Bi 2 ⁢Te 3 interface at low temperature

Topological insulator–magnetic insulator (TI–MI) heterostructures hold significant promise in the field of spintronics, offering the potential for manipulating magnetization through topological surface state–enabled spin-orbit torque. However, many TI–MI interfaces are plagued by issues such as contamination within the magnetic insulator layer and the presence of a low-density transitional region of the topological insulator. These interfacial challenges often obscure the intrinsic behavior of the TI–MI system. In this study, we addressed these challenges by depositing sputtered Bi 2 ⁢Te 3 on liquid phase epitaxy grown Y 3 ⁢Fe 5 ⁢O 12 /Gd 3 ⁢Ga 5 ⁢O 12 . The liquid phase epitaxy grown Y 3 ⁢Fe 5 ⁢O 12 has been previously shown to have exceptional interface quality, without an extended transient layer derived from interdiffusion processes of the substrate or impurity ions, thereby eliminating rare-earth impurity-related losses in the MI at low temperatures. At the TI–MI interface, high-resolution depth-sensitive polarized neutron reflectometry confirmed the absence of a low-density transitional growth region of the TI. By overcoming these undesirable interfacial effects, we isolate and probe the intrinsic low-temperature magnetization dynamics and transport properties of the TI–MI interface. In conclusion, our findings revealed strong spin pumping at low temperatures, accompanied by an additional in-plane anisotropy. The enhanced spin pumping at low temperatures is correlated with the observed suppression of bulk conduction and the weak antilocalization in the TI film, highlighting the interplay between the transport and spin pumping behavior in the TI–MI system.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré WS 2 /WSe 2 heterobilayer

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS 2 /WSe 2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Tunneling spectroscopy of c -axis epitaxial cuprate junctions

Atomically precise epitaxial structures are unique systems for tunneling spectroscopy that minimize extrinsic effects of disorder. We present a systematic tunneling spectroscopy study, over a broad doping, temperature, and bias range, in epitaxial c-axis La 2-x Sr x CuO 4 /La 2 CuO 4 /La 2-x Sr x CuO 4 heterostructures. The behavior of these superconductor/insulator/superconductor (SIS) devices is unusual. Down to 20 mK there is complete suppression of c-axis Josephson critical current with a barrier of only 2 nm of La 2 CuO 4 , and the zero-bias conductance remains at 20–30% of the normal-state conductance, implying a substantial population of in-gap states. Tunneling spectra show greatly suppressed coherence peaks. Furthermore, as the temperature is raised, the superconducting gap fills in rather than closing at T c . For all doping levels, the spectra show an inelastic tunneling feature at ~80 meV, suppressed as T exceeds T c . These nominally simple epitaxial cuprate junctions deviate markedly from expectations based on the standard Bardeen-Cooper-Schrieffer theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗