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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Perovskite Photocatalytic CO 2 Reduction or Photoredox Organic Transformation?

Abstract Metal‐halide perovskites have been explored as photocatalysts for CO 2 reduction. We report that perovskite photocatalytic CO 2 reduction in organic solvents is likely problematic. Instead, the detected products (i.e., CO) likely result from a photoredox organic transformation involving the solvent. Our observations have been validated using isotopic labeling experiments, band energy analysis, and new control experiments. We designed a typical perovskite photocatalytic setup in organic solvents that led to CO production of up to ≈1000 μmol g −1 h −1 . CO 2 reduction in organic solvents must be studied with extra care because photoredox organic transformations can produce orders of magnitude higher rate of CO or CH 4 than is typical for CO 2 reduction routes. Though CO 2 reduction is not likely to occur, in situ CO generation is extremely fast. Hence a suitable system can be established for challenging organic reactions that use CO as a feedstock but exploit the solvent as a CO surrogate.

San Martin, Jovan↗
DOE OSTI2022

Perovskite Photocatalytic CO 2 Reduction or Photoredox Organic Transformation?

Abstract Metal‐halide perovskites have been explored as photocatalysts for CO 2 reduction. We report that perovskite photocatalytic CO 2 reduction in organic solvents is likely problematic. Instead, the detected products (i.e., CO) likely result from a photoredox organic transformation involving the solvent. Our observations have been validated using isotopic labeling experiments, band energy analysis, and new control experiments. We designed a typical perovskite photocatalytic setup in organic solvents that led to CO production of up to ≈1000 μmol g −1 h −1 . CO 2 reduction in organic solvents must be studied with extra care because photoredox organic transformations can produce orders of magnitude higher rate of CO or CH 4 than is typical for CO 2 reduction routes. Though CO 2 reduction is not likely to occur, in situ CO generation is extremely fast. Hence a suitable system can be established for challenging organic reactions that use CO as a feedstock but exploit the solvent as a CO surrogate.

14 SOLAR ENERGY↗
DOE OSTI2024

Dynamic Nanocrystal Superlattices with Thermally Triggerable Lubricating Ligands

The size-dependent and collective physical properties of nanocrystals (NCs) and their self-assembled superlattices (SLs) enable the study of mesoscale phenomena and the design of metamaterials for a broad range of applications. However, the limited mobility of NC building blocks in dried NCSLs often hampers the potential for employing postdeposition methods to produce high-quality NCSLs. In this study, we present tailored promesogenic ligands that exhibit a lubricating property akin to thermotropic liquid crystals. The lubricating ability of ligands is thermally triggerable, allowing the dry solid NC aggregates deposited on the substrates with poor ordering to be transformed into NCSLs with high crystallinity and preferred orientations. The interplay between the dynamic behavior of NCSLs and the molecular structure of the ligands is elucidated through a comprehensive analysis of their lubricating efficacy using both experimental and simulation approaches. Coarse-grained molecular dynamic modeling suggests that a shielding layer from mesogens prevents the interdigitation of ligand tails, facilitating the sliding between outer shells and consequently enhancing the mobility of NC building blocks. Further, the dynamic organization of NCSLs can also be triggered with high spatial resolution by laser illumination. The principles, kinetics, and utility of lubricating ligands could be generalized to unlock stimuli-responsive metamaterials from NCSLs and contribute to the fabrication of NCSLs.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
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 OSTI2021

Structural and magnetic properties of iodide-mediated chemically synthesized L1 2 FePt 3 nanoparticles

In this work, we study the effect of elemental iodine as a halide intermediary in the synthesis of FePt 3 nanoparticles using a co-reduction of Fe(acac) 3 and (NH 4 ) 2 PtCl 2 with 1,2-hexadecanediol. Our study shows that elemental iodine facilitates the formation of FePt 3 nanoparticles with the L1 2 structure. When iodine is not used, the as-made nanoparticles have mostly the disordered fcc FePt 3 structure. The as-made nanoparticles are ferromagnetic and have a Curie temperature close to 380 K. Annealing of the as-made nanoparticles leads to an increased particle size and a transformation to the ordered L1 2 FePt 3 phase. Nanoparticles annealed at 700°C for 30 minutes show a mixture of two magnetic phases, a ferromagnetic phase with a lower ordering temperature of ~300 K and an antiferromagnetic phase with a Néel temperature around 135 K.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Metastable–solid phase diagrams derived from polymorphic solidification kinetics

Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal–liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. Additionally, a rigorous methodology is developed that allows for practical calculations of nucleation rates into arbitrary SCL basins from the undercooled melt. It is demonstrated that at large undercoolings, phase selections made during the nucleation stage can be undone by kinetic instabilities amid the growth stage. On these bases, a solidification–kinetic phase diagram is drawn for the model fcc system that delimits the conditions for macroscopic grains of metastable bcc phase to grow from the melt. We conclude with a study of unconventional interfacial kinetics at special interfaces, which can bring about heterogeneous multiphase crystal growth. A first-order interfacial phase transformation accompanied by a growth-mode transition is examined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Addressing Human and Organizational Factors in Nuclear Industry Modernization: An Operationally Focused Approach to Process and Methodology

Utility owners and operators of commercial nuclear power plants in the United States (U.S.) are and will be modernizing their nuclear power plants by performing a digital transformation involving design of an integrated set of systems that together enable a technology centric operating plant. The Plant Modernization Pathway of the U.S. Department of Energy Light Water Reactor Sustainability Program has a strategic action plan that lays the groundwork for a digital transformation of the nuclear industry. The model for this transformation is an advanced concept of operations, with an end point vision, “To achieve the maximum aggregate benefit enabled by this digital transformation.” To achieve this, the digital infrastructure for a nuclear plant must be designed as an integrated set of systems that together enable a technology centric operating model. The digital transformation process obviously needs to involve technology considerations and systems engineering, but it also needs to include human and organizational expertise. Thus, human and organizational factors, including sociotechnical systems methods and techniques (e.g., Cognitive Systems Engineering, Systems Theoretic Accident Modeling and Processes, human systems integration, and Macroergonomics) need to be considered for digital transformation projects in order to effectively integrate human and organizational expertise efforts into the new work system that results from nuclear power plant digital modernization. That is, the work system is the basic unit of sociotechnical systems analysis and contains three components: personnel, technical, and organization and management. These components should be jointly optimized with respect to the interdependence of systems performance criteria of effectiveness, efficiency and safety. Joint optimization can be achieved through the application of three human and organization functions: knowledge representation, knowledge elicitation, and cross-functional integration. This report provides a strategic framework for effective integration of human and organizational expertise within nuclear power plant digital modernization efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Microchannel-based Membrane-less Extraction of Li from Unconventional Lithium Sources & the Separation of REE

This final report provides an overview of the Project's entire duration, covering July 1, 2021 to December 31, 2023. It primarily focuses on the achievements, technological developments, and unique challenges the team faced while working on separating and extracting Lithium from produced waters. The project's primary aim was to create an integrated, high-throughput, membrane-less, and modular microfluidic platform that could extract Lithium from unconventional sources. We have successfully met all goals and milestones envisioned in the SOPO document. The most critical primary milestones, including the Go-No-Go milestone (refer to the Gantt chart in the Appendices), were successfully accomplished. We demonstrated phase separation (>90%) and extraction (>85%) performance in the MPSE using synthetic, and representative produced water composition feed at 50 ml/min total flow through MPSE 36. We have also performed a parametric study of the MPSE operations, beyond the scope of SOPO, exploring operating conditions of current and broader interest. The extended investigation of operational parameters is concurrent with our efforts to seek further development of the MPSE technology beyond the scope of the Project. Along these lines of development, we have made efforts to be responsive to DOE calls for technological developments of other types of resources (beyond PW) for the recovery of Critical Materials and higher TRL development (beyond TRL 4). During the work on this Project, we developed and implemented three innovative technical approaches that emerged from our efforts to successfully meet the Project milestones. The innovative & original technical approaches developed and implemented in this Project are now the contributions to process engineering that could be clearly credited to the Project. First, Convergent Design Approach is a comprehensive feedforward & feedback loop of four design phases: i) design for functionality, ii) design for manufacturing, iii) design for sustainability, and iv) design for market. Next was Process Intensification. A major aim of this Project was to create an innovative phase separation & extraction microscale-based technology for Li separation – thus the words microchannel-based in the Project title. A microscale-based technology is intrinsically in the center of the Process Intensification domain as defined by its unique principles. Therefore, Process Intensification was implicitly envisioned in the Project’s SOPO. Lastly, Time Scale Analysis is a novel tool for discovering the needs and directions of Process Intensification implementations in any process technology. This Project is fully credited for developing and implementing the three novel technical approaches mentioned above. These are general contributions to process engineering that emerged from this Project. Beyond the original SOPO scope, the OSU-U.Pitt research group utilized a Convergent Design methodology, integrating first-principles mathematical modeling with experimental validation on the Minimum Development Vehicle. By creating these Digital Twins, the team rapidly assessed manufacturing iterations to support TEA analysis. This framework further enabled the development of advanced Surface Modification Techniques, where hydrophobic and oleophobic coating strategies were optimized via Digital Twin tools and validated through rigorous 100-hour longevity testing. TEA Analysis: The closing efforts of this Project were focused on the TEA analysis. TEA analysis had two primary functions: i) enabling critical assessments of design variations withing 10 the Concurrent Design Approach, thus enabling evolution of the MPSE design to reach faster- better-cheaper alternatives; and ii) to create a bridge between the accomplishments of this Project and future projects of higher TRL, beyond TRL 6 level. It is important to note that the TEA model created in the Project stirred the technological solutions for the recovery of critical materials toward a vision of a very profitable modular plant that has unique zero-waste water discharge signature. More importantly, thanks to our experimental performance data and conservative assumptions, the TEA model predicts minimal technological and investment risks. Low cost of a modular unit of a nominal capacity of [1000 tons of Li 2 CO 3 /year] positions the MPSE based technology within the reach of community investors, thus offering a paradigm shift in the development of critical technologies. The project successfully navigated two primary challenges: solvent selection and manufacturing adaptation. Restricted by the SOPO to existing literature for lithium recovery, the team identified a critical need for a "material excellence program" to develop next-generation solvents, eventually concluding with a preliminary investigation into promising Ionic Liquids (ILs). Simultaneously, COVID-19 supply chain disruptions forced a pivot from traditional manufacturing to advanced additive methods at ATAMI-OSU. By transitioning from stainless steel to 3D-printed polymer substrates, the team achieved a transformative three-order-of- magnitude reduction in manufacturing costs and compressed prototyping timelines from several months to just two days. The MPSE technology offers significant energy, environmental, and economic advantages by overcoming the traditional bottlenecks of phase-separation hardware and contactor size. Unlike conventional mixer-settlers or membrane-based systems, MPSE operates without moving parts or fouling-prone membranes, achieving robust performance even with challenging, viscous, or particulate-heavy feeds. Key performance metrics include an energy intensity reduction of 5–50x (3–40 kJ/m 3 ) compared to incumbent technologies and a dramatic reduction of processing time to under 60 seconds, which drastically reduces the physical plant footprint. These technical efficiencies translate into superior economic outcomes; for a 100 t/year Li 2 CO 3 facility, implementing MPSE is projected to nearly halve contactor CAPEX (from $\$$6.08M to $\$$3.01M) and significantly increase the project's Net Present Value (NPV), derisking new investment and enabling distributed critical-mineral processing configurations. The commercialization of MPSE technology is being spearheaded by Vigsur Dynamics Inc., which has adopted a structured, parallel approach to technical and business development since its formation in January 2026. Following extensive customer discovery and engagement with the Oregon State University accelerator, Vigsur Dynamics is working to establish a business model that transitions from pilot demonstrations to modular hardware sales, ultimately aiming for a "build-own-operate" service strategy. Current technical milestones—including 100 hours of continuous operation, superior energy efficiency, and successful 6-unit modular scale-up— provide a foundation for this transition. Backed by ongoing IP licensing and a growing network of industrial and venture advisors, the company is actively de-risking the platform to replace conventional mixer-settler systems in the critical minerals market.

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

Pressure-induced cation and vacancy disorder-order transition and near-zero τ f in deficient hexagonal perovskite Ba 8 ZnTa 6 O 24 dielectrics

Pressure applications can enable the tuning of atomic/defect ordering and provide access to new functional materials. Here, in this study, we report that pressure-induced structural transformation featuring disorder-order transition of both cations and vacancies in the 8-layer deficient hexagonal perovskite tantalate dielectrics Ba 8 ZnTa 6 O 24 , which transformed the structure from twin to shift and remarkably lowered the temperature coefficient of resonant frequency τ f down to near zero (∼0.56 ppm/°C) from 38 ppm/°C for the twinned precursor. The atomic scale STEM-HAADF and EDS results confirm the ordering of Zn in the Ta host at the nanometer scale in the shifted material featuring well-ordered Ba 8 ZnTa 6 O 24 slabs intergrown with Ba 3 ZnTa 2 O 9 and Ba 5 Ta 4 O 15 monolayers and anti-phase grain boundaries as planar defects. The pressure-induced twin-shift structural transformation of Ba 8 ZnTa 6 O 24 features the rare constant concentration of the hexagonal stacked layers, which is allowed by the vacancy ordering at the central layers of face-shared octahedral (FSO) trimers avoiding the FSO B-B repulsion, and remarkably the faster cationic ordering kinetics compared with the 2:1 ordered complex perovskites. Although the inclusion of numerous planar defects and the oxidizable atomic defects led to significant p-type conduction and inhomogeneous electrical microstructures, resulting in an extraordinarily high extrinsic dielectric loss for the high-pressure shifted Ba 8 ZnTa 6 O 24 pellet, the intrinsically near-zero τ f could make the shifted Ba 8 ZnTa 6 O 24 perovskite an ideal microwave dielectric resonator candidate if the defects could be eliminated.

high pressure↗
DOE OSTI2021

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

The Generalized Falk Method (GFM) for coordinate transformation, together with two model-reduction strategies based on this method, are presented for efficient coupled field-circuit simulations. Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors, called trial vectors, to construct a vector basis for coordinate transformation. The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems. We also show that, unlike the Pad´e-via-Lanczos (PVL) method, the GFM does not generate unstable positive poles while reducing the order of circuit problems. Further, the proposed GFM is also faster when compared to methods of the type Lanczos (or Krylov) that are already widely used in circuit simulations for electrothermal and electromagnetic problems. The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods. Further, we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system. The implementation of these equivalent circuit networks in circuit simulators is discussed. With the proposed model-reduction strategies, significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

42 ENGINEERING↗
DOE OSTI2020

Giant anisotropic magnetoresistance in oxygen-vacancy-ordered epitaxial La 0.5 Sr 0.5 CoO 3–δ films

Recent advances in complex oxide heterostructures have realized extraordinary control over oxygen vacancies ($V_\text{O}$), including strain-tuned $V_\text{O}$ order, and electric-field-controlled transformations between perovskite and $V_\text{O}$-ordered structures. Perovskite cobaltites such as La 1– x Sr x CoO 3–δ provide a prime example, recent work demonstrating that strain engineering of $V_\text{O}$ ordering induces large (~10 7 erg/cm 3 ) perpendicular magnetic anisotropy. Here we show that $V_\text{O}$-ordered epitaxial La 0.5 Sr 0.5 CoO 3–δ films exhibit not only strong magnetic anisotropy, but also a giant form of anisotropic magnetoresistance (AMR). This has magnetic field, temperature, and angular dependencies in quantitative accord with conventional AMR, but with AMR ratios up to an extraordinary 40.3%, 20 times enhanced over bulk cobaltites, and ~10–100 times larger than typical transition metals. This giant AMR has no strong dependence on heteroepitaxial strain (between –2.1% and +1.8%) or thickness, and is instead ascribed to symmetry lowering associated with $V_\text{O}$ ordering. The AMR ratios thus obtained in this work are among the largest reported in the over 160-year history of this phenomenon, despite the absence of heavy elements.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nucleation and growth of polar clusters with in-phase tilts into a long-range ferroelectric matrix in a sodium niobate based complex relaxor

In this study, we have investigated the temperature dependence of atomic ordering at multiple length scales in a lead-free sodium niobate-based relaxor, i.e., 0.75 NaNbO 3 -0.25 Ba 0.9⁢ Ca 0.1⁢ TiO 3 (NN-25BCT) via synchrotron x-ray diffraction, Raman spectroscopy, and pair distribution function analysis. High-resolution synchrotron x-ray powder diffraction (SXRD) measurements reveal a ferroelectric phase transition in the relaxor ferroelectric NN-25BCT below the Vogel-Fulcher freezing temperature (𝑇 VF ≈ 270 K). In addition, SXRD analysis demonstrates the competition between in-phase octahedral tilting and ferroelectric order at the long-range scale using mode crystallography. On the other hand, Raman spectroscopic analysis provides evidence of polar ordering for 𝑇 > 𝑇 VF (with tetragonal symmetry) persisting up to the Burns temperature (𝑇 B ). Furthermore, pair distribution function (PDF) analysis reveals the presence of a polar antiferrodistortive tetragonal phase with 𝑃⁢4⁢𝑏𝑚 space group at short ranges throughout the studied temperatures (i.e., 110 K ≤ 𝑇 ≤500 K), irrespective of nonpolar long-range ordering above 𝑇 VF . Therefore, our measurements provide direct evidence for the presence of polar ordering at short ranges and their gradual transformation into long-range polar ordering using an integrated multiscale structural analysis. In conclusion, as a result of a transition from relaxor to a ferroelectric phase in the vicinity of room temperature, NN-25BCT can be exploited for applications in pyroelectric detectors, electrocaloric devices, and multilayered ceramic capacitors.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ordering in liquid and its heredity impact on phase transformation of Mg-Al-Ca alloys

It is a long-sought goal to achieve desired mechanical properties through tailoring phase formation in alloys, especially for complicated multi-phase alloys. In fact, unveiling nucleation of competitive crystalline phases during solidification hinges on the nature of liquid. Here we employ ab initio molecular dynamics simulations (AIMD) to reveal liquid configuration of the Mg-Al-Ca alloys and explore its effect on the transformation of Ca-containing Laves phase from Al 2 Ca to Mg 2 Ca with increasing Ca/Al ratio (r Ca/Al ). There is structural similarity between liquid and crystalline phase in terms of the local arrangement environment, and the connection schemes of polyhedras. The forming signature of Mg 2 Ca, as hinted by the topological and chemical short-range order originating from liquid, ascends monotonically with increasing r Ca/Al . However, Al 2 Ca crystal-like order increase at first and then decrease at the crossover of r Ca/Al = 0.74, corresponding to experimental composition of phase transition from Al 2 Ca to Mg 2 Ca. The origin of phase transformation across different compositions lies in the dense packing of atomic configurations and preferential bonding of chemical species in both liquid and solid. The present finding provides a feasible scenario for manipulating phase formation to achieve high performance alloys by tailoring the crystal-like order in liquid.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Origin of enhanced performance when Mn-rich rocksalt cathodes transform to δ -DRX

Most Mn-rich cathodes are known to undergo phase transformation into structures resembling spinel-like ordering upon electrochemical cycling. Recently, the irreversible transformation of Ti-containing Mn-rich disordered rock-salt cathodes into a phase — named δ — with nanoscale spinel-like domains has been shown to increase energy density, capacity retention, and rate capability. However, the nature of the boundaries between domains and their relationship with composition and electrochemistry are not well understood. In this work, we discuss how the transformation into the multi-domain structure results in eight variants of Spinel domains, which is crucial for explaining the nanoscale domain formation in the δ -phase. We study the energetics of crystallographically unique boundaries and the possibility of Li-percolation across them with a fine-tuned CHGNet machine learning interatomic potential. Energetics of 16 d vacancies reveal a strong affinity to segregate to the boundaries, thereby opening Li-pathways at the boundary to enhance long-range Li-percolation in the δ structure. Defect calculations of the relatively low-mobility Ti show how it can influence the extent of Spinel ordering, domain morphology and size significantly; leading to guidelines for engineering electrochemical performance through changes in composition.

Anand, Shashwat↗
DOE OSTI2025

A dissipation-induced superradiant transition in a strontium cavity-QED system

Driven-dissipative many-body systems are ubiquitous in nature and a fundamental resource for quantum technologies. However, they are also complex and hard to model because they cannot be described by the standard tools in equilibrium statistical mechanics. Probing nonequilibrium critical phenomena in pristine setups can illuminate fresh perspectives on these systems. Here, we use an ensemble of cold 88 Sr atoms coupled to a driven high-finesse cavity to study the cooperative resonance fluorescence (CRF) model, a classic driven-dissipative model describing coherently driven dipoles superradiantly emitting light. We observe its nonequilibrium phase diagram characterized by a second-order phase transition. Below a critical drive strength, the atoms quickly reach the so-called superradiant steady state featuring a macroscopic dipole moment; above the critical point, the atoms undergo persistent Rabi-like oscillations. At longer times, spontaneous emission transforms the second-order transition into a discontinuous first-order transition. Our observations pave the way for harnessing robust entangled states and exploring boundary time crystals in driven-dissipative systems.

Science & Technology - Other Topics↗
DOE OSTI2022

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor ??-(ET)2Cu(NCS )2 , with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order parameter into Abrikosov-like states of higher Landau levels.

Kotte, Tommy↗