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Variation in supercurrent connectivity and vortex pinning of state-of-the-art pulsed laser deposited RE Ba 2 Cu 3 O 7- x coated conductors

REBa 2 Cu 3 O 7-x (REBCO, RE: rare earth) coated conductors (CCs) suffer from great critical current I c differences between different manufacturers, I c variations within individual manufacturers, and often significant lengthwise fluctuations. The understanding of such variations is complicated by the lack of a direct correlation between I c and the critical current density J c . In fact, although J c is the fundamental property determined by the local vortex pinning landscape, I c is often limited by variable current blocking mechanisms. An important practical complexity is commercial practices of performing J c and I c evaluations based on I c at 77 K and self-field (sf), where connectivity variation dominates over vortex pinning variations. However, at higher fields and lower temperatures, vortex pinning becomes more complex and highly variable, making predictions of I c and J c at arbitrary temperature T, magnetic field H, and field orientation θ, quite uncertain. To address some aspects of this problem, we conducted detailed spool-to-spool performance characterization on recently manufactured REBCO CCs. Despite J c (77 K, sf) varies by only ∼11%, J c (77 K, 1 T) of its minimum and maximum (for H//ab-plane) show variations of ∼21% and ∼32%, respectively. This emphasizes the shortcoming in using J c (77 K, sf) as parameter for evaluating even the low field performance. An even more remarkable spool-to-spool J c variation of ∼68% was observed at 20 K and 15 T for H//ab-plane. To identify the origin of such lack of reproducibility we performed microstructural characterizations, which revealed, within the REBCO layer, large variation in the density of copper oxide (CuO x ) particles ranging from 0.1 to 2 μm in size. We believe that they play a decisive role in reducing the effective cross-section of the REBCO layer by not simply blocking current themselves, but also by nucleating off-axis REBCO grains, whose misoriented grain boundaries adversely impact REBCO grain-to-grain connectivity. The REBCO growth associated with high density CuO x particles also leads to the more disordered spatial arrangement of BaHfO 3 precipitate arrays, which, when self-aligning along the ab-planes, generate stronger pinning enhancing J c (H//ab) at all temperatures. In this way, we established that variations of both connectivity and vortex pinning are thus directly coupled. Our results also explain why the so-called ‘lift-factor’, typically defined by the ratio between I c (T, H) and I c (77 K, sf), frequently turns out to be unreliable.

36 MATERIALS SCIENCE↗

Modeling Coupled Chemo-Mechanical Behavior of Randomly Oriented NMC811 Polycrystalline Li-Ion Battery Cathodes

This paper develops a three-dimensional, transient, chemo-mechanical model that predicts the performance of single secondary particle Li-ion battery cathodes. The secondary particles are composed of numerous (approximately 60) randomly oriented single-crystal primary particles. The model incorporates concentration-dependent and anisotropic material properties. As much as possible, electrochemical, transport, and structural properties for crystalline NMC811 (Li x Ni 0.8 Mn 0.1 Co 0.1 O 2 ) are taken from prior publications. Weak Van der Waals bonding between primary particles is modeled empirically using a spring analogy, which enables local primary-particle separations (disintegration) and subsequent reattachments. The model fully couples Li diffusion and the mechanical response. Results include predictions of local Li-concentrations and stresses. High stresses are found near grain boundaries, especially when the lattice orientations are greatly misaligned. Particle separations are characterized in terms of a damage parameter. The model is used to predict the effects of design and operating conditions, including charge/discharge rates, cycling scenarios, and particle sizes.

25 ENERGY STORAGE↗

Modeling Electrodeposition in 3D Porous Architectures for Solid-State Li-Metal Batteries

Li-metal storage in three-dimensional (3D) electrodes is considered a potential dendrite-mitigation strategy. The large surface area and high porosity of these electrodes result in reduced local Li-plating current densities. The porous topology provides a scaffold for Li-deposition and stripping, maintaining both mechanical integrity and Li accessibility. The goal of this study is to understand how characteristics, such as geometry and material properties, affect the current distribution and deposition pattern. To this end, we developed a computational method to track material growth driven by electrodeposition within a complex geometry. This method ensures that the finite-element discretization remains conforming to the moving boundary while preserving an adequate mesh quality, and thus maintains solution accuracy. Using this new computational tool, we analyze the conditions under which porous anode architectures effectively expand the surface area of the charge-transfer interface, and self-regulate current density and dendrite growth.

3D electrode architectures↗

Assessing the Impact of a Novel TBC Material on Heat Transfer in a Spark Ignition Engine through 3D CFD-FEA Co-Simulation Routine

Thermal barrier coatings (TBCs) have been of interest since the 1970s for application in internal combustion (IC) engines. Thin TBCs exhibit a temperature swing phenomenon wherein wall temperatures dynamically respond to the transient working-gas temperature throughout the engine cycle, thus reducing the temperature difference driving the heat transfer. Determining these varying wall temperatures is necessary to evaluate and study the effect of coatings on wall heat transfer. This study focuses on developing a 3D computational fluid dynamics (CFD)-finite element analysis (FEA) coupled simulation, or co-simulation, routine to determine the wall temperatures of a piston coated with a thin TBC layer subject to spark ignition combustion heat flux. A CONVERGE 3D-CFD model was used to simulate the combustion process in a single-cylinder, light-duty experimental spark ignition (SI) engine. Transient piston heat transfer analysis was conducted using ABAQUS, a FEA package, under the simulated combustion heat flux load. The effect of the temperature swing phenomenon due to this TBC layer was observed in a CFD simulation by implementing the FEA results as the piston thermal boundary conditions. The boundary conditions were passed between the CFD and FEA tools until a quasi-steady state solution was achieved. Furthermore, a reduction in wall heat transfer was observed due to a reduced temperature difference between the wall and the working gas.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

ImpactX v0.1

ImpactX is the next generation of the IMPACT-Z code. It is a s-based simulation code for modeling intense beams in particle accelerators using symplectic tracking methods and includes collective effects. It is multi-node parallel and supports modern compute hardware such as GPUs, modern algorithms such as mesh-refinement and realistic geometries (embedded boundaries).

Huebl, Axel↗

Understanding Low Level Jets in the US Atlantic Offshore

Low level jets (LLJs) in the atmosphere exhibit a local windspeed maximum in the boundary layer, with positive shear beneath the jet and negative shear above the jet. Wind turbines tend to experience increased loads with varying wake recovery characteristics in the presence of an LLJ, therefore understanding the mechanism and impact of LLJs is crucial to wind energy development. The US Mid-Atlantic offshore region is a huge potential wind energy resource, yet LLJs in this area are poorly understood. In particular, the coastal offshore environment does not exhibit the same diurnal cycle that leads to strong LLJs in the well-characterized Great Plains region. In this study, we use the Weather Research and Forecasting model (WRF) plus lidar buoy data to identify case studies for LLJ events in 2020 in the New York Bight. A reduced order model is presented to explain the onset of these events based on the competing effects of baroclinicity and eddy diffusivity. Finally, using the macro-scale WRF, we drive a micro-scale large eddy simulation (LES) to generate a more detailed characterization of the Marine Boundary Layer during an LLJ. Gaining a better understanding of LLJs and their impacts on offshore wind in the mid-Atlantic is crucial for a transition toward renewable energy.

atmospheric boundary layer↗

Long-range transported North American wildfire aerosols observed in marine boundary layer of eastern North Atlantic

Wildfire is a major source of biomass burning aerosols, which greatly impact Earth climate. Tree species in North America (NA) boreal forests can support high-intensity crown fires, resulting in elevated injection height and longer lifetime (on the order of months) of the wildfire aerosols. Given the long lifetime, the properties of aged NA wildfire aerosols are required to understand and quantify their effects on radiation and climate. Here we present comprehensive characterization of climatically relevant properties, including optical properties and cloud condensation nuclei (CCN) activities of aged NA wildfire aerosols, emitted from the record-breaking Canadian wildfires in August 2017. Despite the extreme injection height of ~12 km, some of the wildfire plumes descended into the marine boundary layer in the eastern North Atlantic over a period of ~2 weeks, owing to the dry intrusions behind mid-latitude cyclones. The aged wildfire aerosols have high single scattering albedos at 529 nm (ω 529 ; 0.92–0.95) while low absorption Ångström exponents (Å abs ) at 464 nm/648 nm (0.7–0.9). In comparison, Å abs of fresh/slightly aged ones are typically 1.4–3.5. This low Å abs 529 and low Å abs ~110 nm diameter) with thick non-absorbing coatings. The accelerated descent of the wildfire plume also led to strong increase of CCN concentration at the supersaturation levels representative of marine low clouds. The hygroscopicity parameter, κ CCN , of the aged wildfire aerosols varies from 0.2 to 0.4, substantially lower than that of background marine boundary layer aerosols. However, the high fraction of particles with large diameter (i.e., within accumulation size ranges, ~100–250 nm) compensates for the low values of κ, and as a result, the aged NA wildfire aerosols contribute more efficiently to CCN population. These results provide direct evidence that the long-range transported NA wildfires can strongly influence CCN concentration in remote marine boundary layer, therefore the radiative properties of marine low clouds. Given the expected increases of NA wildfire intensity and frequency and regular occurrence of dry intrusion following mid-latitude cyclones, the influence of NA wildfire aerosols on CCN and clouds in remote marine environment need to be further examined.

54 ENVIRONMENTAL SCIENCES↗

A Lagrangian analysis of pockets of open cells over the southeastern Pacific

Abstract. Pockets of open cells (POCs) have been shown to develop within closed-cell stratocumulus (StCu), and a large body of evidence suggests that the development of POCs result from changes in small-scale processes internal to the boundary layer rather than large-scale forcings. Precipitation is widely viewed as a key process important to POC development and maintenance. In this study, GOES-16 satellite observations are used in conjunction with MERRA-2 winds to track and compare the microphysical and environmental evolution of two populations of closed-cell StCu selected by visual inspection over the southeastern Pacific Ocean: one group that transitions to POCs and another comparison group (CLOSED) that does not. The high spatiotemporal resolution of the new GOES-16 data allows for a detailed examination of the temporal evolution of POCs in this region. We find that POCs tend to develop near the coast, last tens of hours, are larger than 104 km2, and often (88 % of cases) do not re-close before they exit the StCu deck. Most POCs are observed to form at night and tend to exit the StCu during the day when the StCu is contracting in area. Relative to the CLOSED trajectories, POCs have systematically larger effective radii, lower cloud drop number concentrations, a comparable conditional in-cloud liquid water path, and a higher frequency of more intense precipitation. Meanwhile, no systematic environmental differences other than boundary layer height are observed between POC and CLOSED trajectories. Interestingly, there are no differences in reanalysis aerosol optical depth between both sets of trajectories, which may lead one to the interpretation that differences in aerosol concentrations are not influencing POC development or resulting in a large number that re-close. However, this largely depends on the reanalysis treatment of aerosol–cloud interactions, and the product used in this study has no explicit handling of these important processes. These results support the consensus view regarding the importance of precipitation on the formation and maintenance of POCs and demonstrate the utility of modern geostationary remote sensing data in evaluating the POC life cycle.

54 ENVIRONMENTAL SCIENCES↗

Effects of transition metal carbide dispersoids on helium bubble formation in dispersion-strengthened tungsten

Abstract The formation of helium bubbles and subsequent property degradation poses a significant challenge to tungsten as a plasma-facing material in future long-pulse plasma-burning fusion reactors. In this study, we investigated helium bubble formation in dispersion-strengthened tungsten doped with transition metal carbides, including TaC, ZrC, and TiC. Of the three dispersoids, TaC exhibited the highest resistance to helium bubble formation, possibly due to the low vacancy mobility in the Group VB metal carbide and oxide phases. Under identical irradiation conditions, large helium bubbles formed at grain boundaries in tungsten, while no bubbles were observed at the interfaces between the carbide dispersoid and tungsten matrix. Moreover, our results showed the interfaces could suppress helium bubble formation in the nearby tungsten matrix, suggesting that the interfaces are more effective in trapping helium as tiny clusters. Our research provided new insights into optimizing the microstructure of dispersion-strengthened tungsten alloys to enhance their performance.

36 MATERIALS SCIENCE↗

Realism of Lagrangian Large Eddy Simulations Driven by Reanalysis Meteorology: Tracking a Pocket of Open Cells Under a Biomass Burning Aerosol Layer

An approach to drive Lagrangian large eddy simulation (LES) of boundary layer clouds with reanalysis data is presented and evaluated using satellite (Spinning Enhanced Visible and Infrared Imager, SEVIRI) and aircraft (Cloud-Aerosol-Radiation Interactions and Forcing, CLARIFY) measurements. The simulations follow trajectories of the boundary layer flow. They track the formation and evolution of a pocket of open cells (POC) underneath a biomass burning aerosol layer in the free troposphere. The simulations reproduce the evolution of observed stratocumulus cloud morphology, cloud optical depth, and cloud drop effective radius, and capture the timing of the cloud state transition from closed to open cells seen in the satellite imagery on the three considered trajectories. They reproduce a biomass burning aerosol layer identified by the in-situ aircraft measurements above the inversion of the POC. Entrainment of aerosol from the biomass burning layer into the POC is limited to the extent of having no impact on cloud- or boundary layer properties, in agreement with the CLARIFY observations. The two-moment bin microphysics scheme used in the simulations reproduces the in-situ cloud microphysical properties reasonably well. A two-moment bulk microphysics scheme reproduces the satellite observations in the non-precipitating closed-cell state, but overestimates liquid water path and cloud optical depth in the precipitating open-cell state due to insufficient surface precipitation. A boundary layer cold and dry bias occurring in LES can be counteracted by reducing the grid aspect ratio and by tightening the large scale wind speed nudging towards the surface.

54 ENVIRONMENTAL SCIENCES↗

Heterogeneous mantle effects on the behavior of SmKS waves and outermost core imaging

Seismic traveltime anomalies of waves that traverse the uppermost 100–200 km of the outer core have been interpreted as evidence of reduced seismic velocities (relative to radial reference models) just below the core–mantle boundary (CMB). These studies typically investigate differential traveltimes of SmKS waves, which propagate as P waves through the shallowest outer core and reflect from the underside of the CMB m times. The use of SmKS and S(m-1)KS differential traveltimes for core imaging are often assumed to suppress contributions from earthquake location errors and unknown and unmodelled seismic velocity heterogeneity in the mantle. The goal of this study is to understand the extent to which differential SmKS traveltimes are, in fact, affected by anomalous mantle structure, potentially including both velocity heterogeneity and anisotropy. Velocity variations affect not only a wave's traveltime, but also the path of a wave, which can be observed in deviations of the wave's incoming direction. Since radial velocity variations in the outer core will only minimally affect the wave path, in contrast to other potential effects, measuring the incoming direction of SmKS waves provides an additional diagnostic as to the origin of traveltime anomalies. Here we use arrays of seismometers to measure traveltime and direction anomalies of SmKS waves that sample the uppermost outer core. We form subarrays of EarthScope's regional Transportable Array stations, thus measuring local variations in traveltime and direction. We observe systematic lateral variations in both traveltime and incoming wave direction, which cannot be explained by changes to the radial seismic velocity profile of the outer core. Moreover, we find a correlation between incoming wave direction and traveltime anomaly, suggesting that observed traveltime anomalies may be caused, at least in part, by changes to the wave path and not solely by perturbations in outer core velocity. Modelling of 1-D ray and 3-D wave propagation in global 3-D tomographic models of mantle velocity anomalies match the trend of the observed traveltime anomalies. Overall, we demonstrate that observed SmKS traveltime anomalies may have a significant contribution from 3-D mantle structure, and not solely from outer core structure.

58 GEOSCIENCES↗

Heterogeneous mantle effects on the behavior of SmKS waves and outermost core imaging

Seismic traveltime anomalies of waves that traverse the uppermost 100–200 km of the outer core have been interpreted as evidence of reduced seismic velocities (relative to radial reference models) just below the core–mantle boundary (CMB). These studies typically investigate differential traveltimes of SmKS waves, which propagate as P waves through the shallowest outer core and reflect from the underside of the CMB m times. The use of SmKS and S(m- 1)KS differential traveltimes for core imaging are often assumed to suppress contributions from earthquake location errors and unknown and unmodelled seismic velocity heterogeneity in the mantle. The goal of this study is to understand the extent to which differential SmKS traveltimes are, in fact, affected by anomalous mantle structure, potentially including both velocity heterogeneity and anisotropy. Velocity variations affect not only a wave’s traveltime, but also the path of a wave, which can be observed in deviations of the wave’s incoming direction. Since radial velocity variations in the outer core will only minimally affect the wave path, in contrast to other potential effects, measuring the incoming direction of SmKS waves provides an additional diagnostic as to the origin of traveltime anomalies. Here we use arrays of seismometers to measure traveltime and direction anomalies of SmKS waves that sample the uppermost outer core. We form subarrays of EarthScope’s regional Transportable Array stations, thus measuring local variations in traveltime and direction. We observe systematic lateral variations in both traveltime and incoming wave direction, which cannot be explained by changes to the radial seismic velocity profile of the outer core. Moreover, we find a correlation between incoming wave direction and traveltime anomaly, suggesting that observed traveltime anomalies may be caused, at least in part, by changes to the wave path and not solely by perturbations in outer core velocity. Modelling of 1-D ray and 3-D wave propagation in global 3-D tomographic models of mantle velocity anomalies match the trend of the observed traveltime anomalies. Overall, we demonstrate that observed SmKS traveltime anomalies may have a significant contribution from 3-D mantle structure, and not solely from outer core structure.

58 GEOSCIENCES↗

Enforcing global constraints for the dispersion closure problem: τ 2 -SIMPLE algorithm

Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on a previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called τ 2 -SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. Furthermore, this algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

97 MATHEMATICS AND COMPUTING↗

Melting and phase relations of Fe-Ni-Si determined by a multi-technique approach

Many studies have suggested silicon as a candidate light element for the cores of Earth and Mercury. However, the effect of silicon on the melting temperatures of core materials and thermal profiles of cores is poorly understood, due to disagreements among melt detection techniques, uncertainties in sample pressure evolution during heating, and sparsity of studies investigating the combined effects of nickel and silicon on the phase diagram of iron. Here, in this study we develop a multi-technique approach for measuring the high-pressure melting and solid phase relations of iron alloys and apply it to Fe 0.8 Ni 0.1 Si 0.1 (Fe-11wt%Ni-5.3wt%Si), a composition compatible with recent estimates for the cores of Earth and Mercury. This approach combines results (20-83 GPa) from two atomic-level techniques: synchrotron Mossbauer spectroscopy (SMS) and synchrotron x-ray diffraction (XRD). Melting is independently detected by the loss of the Mossbauer signal, produced exclusively by solid-bound iron nuclei, and the onset of a liquid diffuse x-ray scattering signal. The use of a burst heating and background updating method for quantifying changes in the reference background during heating facilitates the determination of liquid diffuse signal onsets and leads to strong reproducibility and excellent agreement in melting temperatures determined separately by the two techniques. XRD measurements additionally constrain the hcp-fcc phase boundary and in-situ pressure evolution of the samples during heating. We apply our updated thermal pressure model to published SMS melting data on fcc-Fe and fcc-Fe 0.9 Ni 0.1 to precisely evaluate the effect of silicon on melting temperatures. We find that the addition of 10 mol% Si to Fe 0.9 Ni 0.1 reduces melting temperatures by ~250 K at low pressures (<60 GPa) and flattens the hcp-fcc phase boundary. Extrapolating our results, we constrain the location of the hcp-fcc-liquid quasi-triple point at 147±14 GPa and 3140±90 K, which implies a melting temperature reduction of 500 K compared with Fe 0.9 Ni 0.1 . The results demonstrate the advantages of combining complementary experimental techniques in investigations of melting under extreme conditions.

36 MATERIALS SCIENCE↗

Bubble formation in helium-implanted nanostructured ferritic alloys at elevated temperatures

Helium bubble formation was examined by scanning/transmission electron microscopy (S/TEM) in Fe-9/10Cr binary alloys and two dispersion strengthened nanostructured alloys (CNA3 and 14YWT containing 5–10 nm diameter carbide and oxide particles, respectively) after ex-situ and in-situ He implantation to ~10,000 appm at 500 to 900 °C. The combination of high-resolution STEM images and electron energy loss spectroscopy (EELS) revealed that the Y-Ti-O nanoparticles in 14YWT were uniformly distributed and exhibited a one-to-one relationship for bubble attachment to the nanoclusters. In the in-situ experiment at 900 °C, grain boundary cracking was severe in the Fe-10Cr model alloy, but not in the nanostructured alloys. From 500 to 900 °C, the bubble size generally increased with increasing irradiation temperature, while the bubble density decreased with increasing temperature. At the same temperatures, the bubble size in the implanted materials was in the order of Fe-9/10Cr > CNA3 > 14YWT, while the bubble density showed the opposite order. The observed bubble number densities for the nanostructured alloys are comparable to the nanoparticle density, suggesting that the nanoparticles in both alloys were effective in trapping He. Overall, our results indicate that very high He concentrations can be managed in nanostructured alloys by sequestering the helium into smaller bubbles (which leads to a lower volume swelling value) and to shield He from the grain boundaries. This can be attributed to the much higher sink strength associated with the nanoclusters or the He trapping ability between different types of nanoclusters.

36 MATERIALS SCIENCE↗

Single- and two-particle finite size effects in interacting lattice systems

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an efficient strategy to eliminate one-body finite size effects. In the dynamical mean field community, cluster generalizations of the dynamical mean field theory were formulated to study systems with nonlocal correlations. In this work, we put the twist-averaging and the dynamical cluster approximation variant of the dynamical mean field theory onto equal footing, discuss commonalities and differences, and compare results from both techniques to the standard periodic boundary technique. At the example of Hubbard-type models with local, short-range and Yukawa-like longer range interactions we show that all methods converge to the same limit, but that the convergence speed differs in practice. We show that embedding theories are an effective tool for managing both one-body and two-body finite size effects, in particular if interactions are averaged over twist angles.

36 MATERIALS SCIENCE↗

Vertical dependence of horizontal variation of cloud microphysics: observations from the ACE-ENA field campaign and implications for warm-rain simulation in climate models

Abstract. In the current global climate models (GCMs), the nonlinearity effect of subgrid cloud variations on the parameterization of warm-rain process, e.g., the autoconversion rate, is often treated by multiplying the resolved-scale warm-rain process rates by a so-called enhancement factor (EF). In this study, we investigate the subgrid-scale horizontal variations and covariation of cloud water content (qc) and cloud droplet number concentration (Nc) in marine boundary layer (MBL) clouds based on the in situ measurements from a recent field campaign and study the implications for the autoconversion rate EF in GCMs. Based on a few carefully selected cases from the field campaign, we found that in contrast to the enhancing effect of qc and Nc variations that tends to make EF > 1, the strong positive correlation between qc and Nc results in a suppressing effect that tends to make EF < 1. This effect is especially strong at cloud top, where the qc and Nc correlation can be as high as 0.95. We also found that the physically complete EF that accounts for the covariation of qc and Nc is significantly smaller than its counterpart that accounts only for the subgrid variation of qc, especially at cloud top. Although this study is based on limited cases, it suggests that the subgrid variations of Nc and its correlation with qc both need to be considered for an accurate simulation of the autoconversion process in GCMs.

54 ENVIRONMENTAL SCIENCES↗

Understanding resistance oscillation in the CsV 3 Sb 5 superconductor

A recent demonstration of the periodic oscillation of resistance in the thin film of the CsV 3 ⁢Sb 5 superconductor with a hole in the film suggests that charge-4⁢ e and charge-6⁢⁢ e Cooper pairs may have condensed in this compound. While exciting, such interpretation calls for a precise determination of the effective area for the passage of Cooper pairs from one end of the lead to the other. Unlike the traditional Little-Parks effect where the rim around the hole is thin, the effective hole area is not obviously defined for the “thick-rim geometry” adopted in the experiment. Here, we note that the experiment was conducted in a regime where the superconductivity is strongly fluctuating, which motivates an analysis based on the spacetime formulation of the time-dependent Ginzburg-Landau theory. Further, we argue that under appropriate conditions, the optimal semiclassical path is not the geometrically shortest one, but the one that moves along the edge of the hole and takes advantage of the reduced fluctuations at the boundary of the hole. The condition for the crossover from the geometrically shortest path to the path that sticks to the wall is clarified. In such a scenario, the geometric area of the hole indeed emerges as the effective area for the flux, providing a theoretical justification to the interpretation given by J. Ge et al. (arXiv:2201.10352). The conclusion of our analysis may have implications for similar experiments in other superconductors where the geometry of the device is not obviously that of the Little-Parks experiment employing the thin wall, but of the thick-rim type such as used in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗