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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Gaunt and Breit two-electron contributions to mean-field transformations and fine structure splitting

Materials utilized by novel energy systems are often studied using weakly correlated mean-field theories. However, if these systems incorporate heavy elements, relativistic effects must be included. Therefore, a Kramers unrestricted coupled cluster with singles and doubles excitation formalism within a molecular mean-field exact two-component framework (X2C mmf ) using a four-component Dirac–Hartree–Fock (DHF) reference state is presented. The exact X2C mmf transformed normal-order Hamiltonian incorporates all one-electron and two-electron (2e) contributions from the Coulomb, Gaunt, and Breit operators and is used with the equation of motion method to calculate the excitation energies of the alkali group of elements. Using this framework, the effects of 2e Gaunt and Breit integrals are studied. Results demonstrate growing contributions from these integrals to the generated X2C mmf mean-fields and electronic fine structure calculations with increasing atomic number. Overall, this paper outlines the method, its effect within the X2C mmf approach, and lays the foundation for future theoretical development of relativistic calculations within this framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Barium stars as tracers of s -process nucleosynthesis in AGB stars: II. Using machine learning techniques on 169 stars

Barium (Ba) stars are characterised by an abundance of heavy elements made by the slow neutron capture process (s-process). This peculiar observed signature is due to the mass transfer from a stellar companion, bound in a binary stellar system, to the Ba star observed today. The signature is created when the stellar companion is an asymptotic giant branch (AGB) star. We aim to analyse the abundance pattern of 169 Ba stars using machine learning techniques and the AGB final surface abundances predicted by the FRUITY and Monash stellar models. We developed machine learning algorithms that use the abundance pattern of Ba stars as input to classify the initial mass and metallicity of each Ba star’s companion star using stellar model predictions. We used two algorithms. The first exploits neural networks to recognise patterns, and the second is a nearest-neighbour algorithm that focuses on finding the AGB model that predicts the final surface abundances closest to the observed Ba star values. In the second algorithm, we included the error bars and observational uncertainties in order to find the best-fit model. The classification process was based on the abundances of Fe, Rb, Sr, Zr, Ru, Nd, Ce, Sm, and Eu. We selected these elements by systematically removing s-process elements from our AGB model abundance distributions and identifying the elements whose removal had the biggest positive effect on the classification. We excluded Nb, Y, Mo, and La. Our final classification combined the output of both algorithms to identify an initial mass and metallicity range for each Ba star companion. With our analysis tools, we identified the main properties for 166 of the 169 Ba stars in the stellar sample. The classifications based on both stellar sets of AGB final abundances show similar distributions, with an average initial mass of M = 2.23 M ⊙ and 2.34 M ⊙ and an average [Fe/H] = –0.21 and –0.11, respectively. We investigated why the removal of Nb, Y, Mo, and La improves our classification and identified 43 stars for which the exclusion had the biggest effect. We found that these stars have statistically significant and different abundances for these elements compared to the other Ba stars in our sample. We discuss the possible reasons for these differences in the abundance patterns.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Accurate frozen core approximation for all-electron density-functional theory

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr3 with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below −200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

Yu, Victor Wen-zhe↗
DOE OSTI2022

Efficient evaluation of the Breit operator in the Pauli spinor basis

The frequency-independent Coulomb–Breit operator gives rise to the most accurate treatment of two-electron interaction in the non-quantum-electrodynamics regime. The Breit interaction in the Coulomb gauge consists of magnetic and gauge contributions. The high computational cost of the gauge term limits the application of the Breit interaction in relativistic molecular calculations. In this work, we apply the Pauli component integral–density matrix contraction scheme for gauge interaction with a maximum spin- and component separation scheme. We also present two different computational algorithms for evaluating gauge integrals. One is the generalized Obara–Saika algorithm, where the Laplace transformation is used to transform the gauge operator into Gaussian functions and the Obara–Saika recursion is used for reducing the angular momentum. The other algorithm is the second derivative of Coulomb interaction evaluated with Rys-quadrature. This work improves the efficiency of performing Dirac–Hartree–Fock with the variational treatment of Breit interaction for molecular systems. In conclusion, we use this formalism to examine relativistic trends in the Periodic Table and analyze the relativistic two-electron interaction contributions in heavy-element complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

The paper reports development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), a new relativistic quantum-chemical method for treating spin-orbit coupling in molecules. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. In conclusion, to demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

R-matrix calculations for opacities: I. Methodology and computations

Abstract An extended version of the R -matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the distorted wave approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the opacity project (OP). Among the improvements incorporated are: (i) large-scale Breit–Pauli R -matrix calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the ( e + ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a ‘top-up’ procedure to compare convergence with R -matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound ( e + ion) levels. The present R -matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, opacities of heavy elements might require revisions in high temperature-density plasma sources.

Pradhan, A. K. (ORCID:0000000187753643)↗
DOE OSTI2023

Chiral photocurrent in a Quasi-1D TiS 3 (001) phototransistor

The presence of in-plane chiral effects, hence spin–orbit coupling, is evident in the changes in the photocurrent produced in a TiS 3 (001) field-effect phototransistor with left versus right circularly polarized light. The direction of the photocurrent is protected by the presence of strong spin–orbit coupling and the anisotropy of the band structure as indicated in NanoARPES measurements. As hsown here, dark electronic transport measurements indicate that TiS 3 is n-type and has an electron mobility in the range of 1–6 cm 2 V –1 s –1 . I–V measurements under laser illumination indicate the photocurrent exhibits a bias directionality dependence, reminiscent of bipolar spin diode behavior. Because the TiS 3 contains no heavy elements, the presence of spin–orbit coupling must be attributed to the observed loss of inversion symmetry at the TiS 3 (001) surface.

Phototransistor Materials↗
DOE OSTI2025

Multimuons in cosmic-ray events as seen in ALICE at the LHC

ALICE is a large experiment at the CERN Large Hadron Collider. Located 52 meters underground, its detectors are suitable to measure muons produced by cosmic-ray interactions in the atmosphere. In this paper, the studies of the cosmic muons registered by ALICE during Run 2 (2015–2018) are described. The analysis is limited to multimuon events defined as events with more than four detected muons (N μ > 4) and in the zenith angle range 0° < θ < 50°. The results are compared with Monte Carlo simulations using three of the main hadronic interaction models describing the air shower development in the atmosphere: QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d. The interval of the primary cosmic-ray energy involved in the measured muon multiplicity distribution is about 4 × 10 15 < E prim < 6 × 10 16 eV. In this interval none of the three models is able to describe precisely the trend of the composition of cosmic rays as the energy increases. However, QGSJET-II-04 is found to be the only model capable of reproducing reasonably well the muon multiplicity distribution, assuming a heavy composition of the primary cosmic rays over the whole energy range, while SIBYLL 2.3d and EPOS-LHC underpredict the number of muons in a large interval of multiplicity by more than 20% and 30%, respectively. The rate of high muon multiplicity events (N μ > 100) obtained with QGSJET-II-04 and SIBYLL 2.3d is compatible with the data, while EPOS-LHC produces a significantly lower rate (55% of the measured rate). For both QGSJET-II-04 and SIBYLL 2.3d, the rate is close to the data when the composition is assumed to be dominated by heavy elements, an outcome compatible with the average energy E prim ∼ 10 17 eV of these events. This result places significant constraints on more exotic production mechanisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Convolutional neural network based non-iterative reconstruction for accelerating neutron tomography *

Abstract Neutron computed tomography (NCT), a 3D non-destructive characterization technique, is carried out at nuclear reactor or spallation neutron source-based user facilities. Because neutrons are not severely attenuated by heavy elements and are sensitive to light elements like hydrogen, neutron radiography and computed tomography offer a complementary contrast to x-ray CT conducted at a synchrotron user facility. However, compared to synchrotron x-ray CT, the acquisition time for an NCT scan can be orders of magnitude higher due to lower source flux, low detector efficiency and the need to collect a large number of projection images for a high-quality reconstruction when using conventional algorithms. As a result of the long scan times for NCT, the number and type of experiments that can be conducted at a user facility is severely restricted. Recently, several deep convolutional neural network (DCNN) based algorithms have been introduced in the context of accelerating CT scans that can enable high quality reconstructions from sparse-view data. In this paper, we introduce DCNN algorithms to obtain high-quality reconstructions from sparse-view and low signal-to-noise ratio NCT data-sets thereby enabling accelerated scans. Our method is based on the supervised learning strategy of training a DCNN to map a low-quality reconstruction from sparse-view data to a higher quality reconstruction. Specifically, we evaluate the performance of two popular DCNN architectures—one based on using patches for training and the other on using the full images for training. We observe that both the DCNN architectures offer improvements in performance over classical multi-layer perceptron as well as conventional CT reconstruction algorithms. Our results illustrate that the DCNN can be a powerful tool to obtain high-quality NCT reconstructions from sparse-view data thereby enabling accelerated NCT scans for increasing user-facility throughput or enabling high-resolution time-resolved NCT scans.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

The SDSS/APOGEE catalogue of HgMn stars

ABSTRACT We report on H-band spectra of chemically peculiar Mercury–Manganese (HgMn) stars obtained via the SDSS/APOGEE survey. As opposed to other varieties of chemically peculiar stars such as classical Ap/Bp stars, HgMn stars lack strong magnetic fields and are defined by extreme overabundances of Mn, Hg, and other heavy elements. A satisfactory explanation for the abundance patterns remains to be determined, but low rotational velocity is a requirement and involvement in binary/multiple systems may be as well. The APOGEE HgMn sample currently consists of 269 stars that were identified among the telluric standard stars as those whose metallic absorption content is limited to or dominated by the H-band Mn ii lines. Due to the fainter magnitudes probed by the APOGEE survey as compared to past studies, only 9/269 stars in the sample were previously known as HgMn types. The 260 newly identified HgMn stars represents a more than doubling of the known sample. At least 32 per cent of the APOGEE sample are found to be binary or multiple systems, and from multi-epoch spectroscopy, we were able to determine orbital solutions for at least one component in 32 binaries. Many of the multilined systems include chemically peculiar companions, with noteworthy examples being the HgMn+Ap/Bp binary HD 5429, the HgMn+HgMn binary HD 298641, and the HgMn+Bp Mn + Am triple system HD 231263. As a further peculiarity, roughly half of the sample produces narrow emission in the C i 16895 Å line, with widths and radial velocities that match those of the Mn ii lines.

Chojnowski, S. Drew↗
DOE OSTI2020

Magnesium abundances in cool metal-polluted white dwarfs

ABSTRACT The accretion of rocky material is responsible for the presence of heavy elements in the atmospheres of a large fraction of white dwarf stars. Those objects represent a unique opportunity to infer the bulk composition of exoplanetesimals. This chemical characterization requires the use of detailed atmosphere models to determine the elemental abundances at the photospheres of white dwarfs. In this work, we use a state-of-the-art model atmosphere code to reanalyse the first large survey of metal-polluted white dwarfs for which abundances are found for multiple elements. We show that the improved constitutive physics of our models lead to systematically higher Mg abundances than previous analyses. We find an average $\log \, {\rm Mg/Ca}$ number abundance ratio of 1.5. This value is significantly above the reference abundance for chondrites, which is expected as current diffusion models predict that for the cool helium-atmosphere white dwarfs of our sample, Mg should remain in the atmosphere longer than Ca. This helps resolve a recently identified Mg depletion problem, where the planetesimals accreted by white dwarfs were reported to be Mg-deficient compared to the expected composition of their planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Asteroseismic modelling of solar-type stars: a deeper look at the treatment of initial helium abundance

ABSTRACT Detailed understanding of stellar physics is essential towards a robust determination of stellar properties (e.g. radius, mass, and age). Among the vital input physics used in the modelling of solar-type stars which remain poorly constrained, is the initial helium abundance. To this end, when constructing stellar model grids, the initial helium abundance is estimated either (i) by using the semi-empirical helium-to-heavy element enrichment ratio, (ΔY/ΔZ), anchored to the standard big bang nucleosynthesis value, or (ii) by setting the initial helium abundance as a free variable. Adopting 35 low-mass, solar-type stars with multiyear Kepler photometry from the asteroseismic ‘LEGACY’ sample, we explore the systematic uncertainties on the inferred stellar parameters (i.e. radius, mass, and age) arising from the treatment of the initial helium abundance in stellar model grids. The stellar masses and radii derived from grids with free initial helium abundance are lower compared to those from grids based on a fixed ΔY/ΔZ ratio. We find the systematic uncertainties on mean density, radius, mass, and age arising from grids which employ a fixed value of ΔY/ΔZ and those with free initial helium abundance to be ∼ 0.9 per cent, ∼ 2 per cent, ∼ 5 per cent, and ∼ 29 per cent, respectively. We report that the systematic uncertainties on the inferred masses and radii arising from the treatment of initial helium abundance in stellar grids lie within the expected accuracy limits of ESA’s PLATO, although this is not the case for the age.

Nsamba, Benard↗
DOE OSTI2023

Asteroseismological analysis of the polluted ZZ Ceti star G 29 – 38 with TESS

G29 – 38 (TIC 422526868) is one of the brightest (V = 13.1) and closest (d = 17.51 pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the TESS spacecraft in sectors 42 and 56. The atmosphere of G 29 – 38 is polluted by heavy elements that are expected to sink out of visible layers on short time-scales. Here, the photometric TESS data set spans ~51 d in total, and from this, we identified 56 significant pulsation frequencies, that include rotational frequency multiplets. In addition, we identified 30 combination frequencies in each sector. The oscillation frequencies that we found are associated with g-mode pulsations, with periods spanning from ~ 260 to ~ 1400 s. We identified rotational frequency triplets with a mean separation δν ℓ = 1 of 4.67 μHz and a quintuplet with a mean separation δν ℓ = 2 of 6.67 μHz, from which we estimated a rotation period of about 1.35 ± 0.1 d. We determined a constant period spacing of 41.20 s for ℓ = 1 modes and 22.58 s for ℓ = 2 modes. We performed period-to-period fit analyses and found an asteroseismological model with M * /M ⊙ = 0.632 ± 0.03, K, and log g = 8.048 ± 0.005 (with a hydrogen envelope mass of M H ~ 5.6 × 10 –5 M * ), in good agreement with the values derived from spectroscopy. We obtained an asteroseismic distance of 17.54 pc, which is in excellent agreement with that provided by Gaia (17.51 pc).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

TOI-2374 b and TOI-3071 b: two metal-rich sub-Saturns well within the Neptunian desert

ABSTRACT We report the discovery of two transiting planets detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-2374 b and TOI-3071 b, orbiting a K5V and an F8V star, respectively, with periods of 4.31 and 1.27 d, respectively. We confirm and characterize these two planets with a variety of ground-based and follow-up observations, including photometry, precise radial velocity monitoring and high-resolution imaging. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We found that the two planets have masses of (57 ± 4) M⊕ or (0.18 ± 0.01) MJ, and (68 ± 4) M⊕ or (0.21 ± 0.01) MJ, respectively, and they have radii of (6.8 ± 0.3) R⊕ or (0.61 ± 0.03) RJ and (7.2 ± 0.5) R⊕ or (0.64 ± 0.05) RJ, respectively. These parameters correspond to sub-Saturns within the Neptunian desert, both planets being hot and highly irradiated, with Teq ≈ 745 K and Teq ≈ 1812 K, respectively, assuming a Bond albedo of 0.5. TOI-3071 b has the hottest equilibrium temperature of all known planets with masses between 10 and 300 M⊕ and radii less than 1.5 RJ. By applying gas giant evolution models we found that both planets, especially TOI-3071 b, are very metal-rich. This challenges standard formation models which generally predict lower heavy-element masses for planets with similar characteristics. We studied the evolution of the planets’ atmospheres under photoevaporation and concluded that both are stable against evaporation due to their large masses and likely high metallicities in their gaseous envelopes.

Hacker, Alejandro (ORCID:0009000994520181)↗
DOE OSTI2024

Actinide signatures in low electron fraction kilonova ejecta

ABSTRACT Neutron star (NS) mergers are known to produce heavy elements through rapid neutron capture (r-process) nucleosynthesis. Actinides are expected to be created solely by the r-process in the most neutron-rich environments. Confirming if NS mergers provide the requisite conditions for actinide creation is therefore central to determining their origin in the Universe. Actinide signatures in kilonova (KN) spectra may yield an answer, provided adequate models are available in order to interpret observational data. In this study, we investigate actinide signatures in neutron-rich merger ejecta. We use three ejecta models with different compositions and radioactive power, generated by nucleosynthesis calculations using the same initial electron fraction ($Y_e = 0.15$) but with different nuclear physics inputs and thermodynamic expansion history. These are evolved from 10 to 100 d after merger using the sumo non-local thermodynamic equilibrium (NLTE) radiative transfer code. We highlight how uncertainties in nuclear properties, as well as choices in thermodynamic trajectory, may yield entirely different outputs for equal values of $Y_e$. We consider an actinide-free model and two actinide-rich models, and find that the emergent spectra and light-curve evolution are significantly different depending on the amount of actinides present, and the overall decay properties of the models. We also present potential key actinide spectral signatures, of which doubly ionized $_{89}$Ac and $_{90}$Th may be particularly interesting as spectral indicators of actinide presence in KN ejecta.

Pognan, Quentin (ORCID:0000000152550782)↗
DOE OSTI2026

Uncertainties in the production of iron-group nuclides in core-collapse supernovae from Monte Carlo variations of reaction rates

Core-collapse supernovae, occurring at the end of massive star evolution, produce heavy elements, including those in the iron peak. Although the explosion mechanism is not yet fully understood, theoretical models can reproduce optical observations and observed elemental abundances. However, many nuclear reaction rates involved in explosive nucleosynthesis have large uncertainties, impacting the reliability of abundance predictions. To address this, we have previously developed a Monte Carlo-based nucleosynthesis code that accounts for reaction rate uncertainties and has been applied to nucleosynthesis processes beyond iron. Our framework is also well suited for studying explosive nucleosynthesis in supernovae. In this paper, we investigate 1D explosion models using the ‘PUSH method’ , focusing on progenitors with varying metallicities and initial masses around $M_{\rm ZAMS} = 16\, {\rm M}_{\odot }$. Detailed post-process nucleosynthesis calculations and Monte Carlo analyses are used to explore the effects of reaction rate uncertainties and to identify key reaction rates in explosive nucleosynthesis. We find that many reactions have little impact on the production of iron-group nuclei, as these elements are primarily synthesized in the nuclear statistical equilibrium. However, we identify a few ‘key reactions’ that significantly influence the production of radioactive nuclei, which may affect astrophysical observables. In particular, for the production of ${}^{44}{\rm Ti}$, we confirm that several traditionally studied nuclear reactions have a strong impact. However, determining a single reaction rate is insufficient to draw a definitive conclusion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Crystal structure and thermal expansion of Ta 2 ⁢O 5 from neutron diffraction

Tantalum pentoxide (Ta 2 ⁢O 5 ) is a component of technologies ranging from photographic lenses to medical implants. Despite more than six decades of interest, however, there is no consensus on the crystal structure of Ta 2 ⁢O 5 . Here, we report the results of neutron diffraction experiments on Ta 2⁢ O 5 powders at temperatures up to 1000⁢°⁢C. Because neutron diffraction is sensitive to the positions of O atoms in the presence of heavy elements, our results provide strong evidence that the orthorhombic L SR structure can account for experimental observations better than any other proposal in the literature. Here, we also determine the anisotropic crystallographic thermal expansion parameters of Ta 2 ⁢O 5 , which are important for modeling the performance of Ta 2⁢ O 5 -bearing technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Oxygen vacancy induced electronic structure modification of KTaO 3

The observation of a metallic interface between band insulators LaAlO 3 and SrTiO 3 has led to massive efforts to understand the origin of the phenomenon as well as to search for other systems hosting such two-dimensional electron gases (2-DEGs). However, the understanding of the origin of the 2-DEG is very often hindered as several possible mechanisms such as polar catastrophe, cationic intermixing, and oxygen vacancy (OV) can be operative simultaneously. The presence of a heavy element makes the KTaO 3 (KTO) based 2-DEG a potential platform to investigate spin-orbit coupling driven novel electronic and magnetic phenomena. In this work, we investigate the sole effect of OV in KTO, which makes KTO metallic. O K-edge x-ray absorption spectroscopy measurements find that OV dopes electrons in Ta t * 2g antibonding states. Photoluminescence measurements reveal the existence of a highly localized deep midgap state in oxygen-deficient KTO. Our detailed ab initio calculations demonstrate that such deep midgap state arises due to the linear clustering of OVs around Ta. Finally, our present work emphasizes that we must pay attention to the possible presence of OVs in interpreting emergent behavior of KTO-based heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗