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36 pages, 3688 KB

Open AccessArticle

Quantum Chemistry of Strongly Correlated Electron Systems: Quantum Coherence of Open-Shell Molecular Systems Constructed by Chemical Methods: Organometallic Conjugation and Confinement

by Takashi Kawakami, Satoru Yamada, Masateru Taniguchi and Kizashi Yamaguchi

Quantum Rep. 2026, 8(1), 10; https://doi.org/10.3390/quantum8010010 (registering DOI) - 31 Jan 2026

Abstract

Electronic and spin structures of open-shell molecules and clusters were investigated as possible building blocks for the construction of one- and two-dimensional quantum spin alignment systems which exhibited several characteristic quantum properties of strongly correlated electron systems: high-T_c superconductivity, quantum spin [...] Read more.

Electronic and spin structures of open-shell molecules and clusters were investigated as possible building blocks for the construction of one- and two-dimensional quantum spin alignment systems which exhibited several characteristic quantum properties of strongly correlated electron systems: high-T_c superconductivity, quantum spin coherence, entanglement, etc. Ab initio calculations were performed to elucidate effective exchange integrals (J) for 3d transition metal oxides, providing the J-model for high-T_c superconductivity. Theoretical investigations such as Monte Carlo simulation, molecular mechanics and quantum mechanical calculations were performed to elucidate effective chemical procedures for through-bond alignments of open-shell transition metal ions by organometallic conjugation and through-space confinements of molecular spins such as molecular oxygen by molecular confinement materials. Theoretical simulations have elucidated the importance of appropriate confinement materials for alignments of molecular spins desired for quantum coherence and quantum sensing. Equivalent transformations among coherent states of superconductors, trapped ion, neutral atom, molecular spin, molecular exciton, etc., are also discussed on theoretical and conceptual grounds such as quantum entanglement and decoherence. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)

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13 pages, 705 KB

Open AccessFeature PaperArticle

Magnetic-Field Oscillations of the Critical Temperature in Ultraclean, Two-Dimensional Type-I Superconductors

by Aiying Zhao, Richard A. Klemm and Qiang Gu

Condens. Matter 2025, 10(4), 61; https://doi.org/10.3390/condmat10040061 - 29 Nov 2025

Viewed by 1107

Abstract

We investigate the influence of Landau Levels (LLs) and Zeeman energy, induced by an applied magnetic field

B

, on the critical temperature

T_{c}

for two-dimensional (2D) ultraclean superconductors using a fully quantum mechanical approach within the Bardeen–Cooper–Schrieffer (BCS) theory. In contrast [...] Read more.

We investigate the influence of Landau Levels (LLs) and Zeeman energy, induced by an applied magnetic field

B

, on the critical temperature

T_{c}

for two-dimensional (2D) ultraclean superconductors using a fully quantum mechanical approach within the Bardeen–Cooper–Schrieffer (BCS) theory. In contrast to standard BCS theory, it allows for Cooper pair formation between electrons with opposite spins and momenta along the

B

direction, both on the same or on neighboring LLs. Our quantum mechanical treatment of LLs reveals that the critical temperature

T_{c}

for electrons paired on the same LL exhibits oscillations around the BCS critical temperature at low magnetic fields. The Zeeman energy leads to a decrease in

T_{c} (B)

with increasing

B

for electrons paired both on the same and on neighboring LLs. Notably, as the g-factor increases,

T_{c} (B)

decreases faster as the magnetic field increases for a larger g-factor than for a smaller one. Full article

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19 pages, 2373 KB

Open AccessArticle

Numerical Investigation of Fracture Behavior and Current-Carrying Capability Degradation in Bi2212/Ag Composite Superconducting Wires Subjected to Mechanical Loads Using Phase Field Method

by Feng Xue and Kexin Zhou

Modelling 2025, 6(4), 119; https://doi.org/10.3390/modelling6040119 - 1 Oct 2025

Viewed by 519

Abstract

Bi₂Sr₂CaCu₂O_8+x (Bi2212) high-temperature superconductor exhibits broad application prospects in strong magnetic fields, superconducting magnets, and power transmission due to its exceptional electrical properties. However, during practical applications, Bi2212 superconducting round wires are prone to mechanical [...] Read more.

Bi₂Sr₂CaCu₂O_8+x (Bi2212) high-temperature superconductor exhibits broad application prospects in strong magnetic fields, superconducting magnets, and power transmission due to its exceptional electrical properties. However, during practical applications, Bi2212 superconducting round wires are prone to mechanical loading effects, leading to crack propagation and degradation of superconducting performance, which severely compromises their reliability and service life. To elucidate the damage mechanisms under mechanical loading and their impact on critical current, this study establishes a two-dimensional model with existing cracks based on phase field fracture theory, simulating crack propagation behaviors under varying conditions. The results demonstrate that crack nucleation and propagation paths are predominantly governed by stress concentration zones. The transition zone width of cracks is controlled by the phase field length scale parameter. By incorporating electric fields into the phase field model, coupled mechanical-electrical simulations reveal that post-crack penetration causes significant current shunting, resulting in a marked decline in current density. The research quantitatively explains the mechanism of critical current degradation in Bi2212 round wires under tensile strain from a mechanical perspective. Full article

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23 pages, 937 KB

Open AccessArticle

An Improved Calculation of Bose–Einstein Condensation Temperature

by Andras Kovacs

Mod. Math. Phys. 2025, 1(2), 6; https://doi.org/10.3390/mmphys1020006 - 24 Jul 2025

Viewed by 1088

Abstract

Bose–Einstein condensation is an intensely studied quantum phenomenon that emerges at low temperatures. While preceding Bose–Einstein condensation models do not consider what statistics apply above the condensation temperature, we show that neglecting this question leads to inconsistencies. A mathematically rigorous calculation of Bose–Einstein [...] Read more.

Bose–Einstein condensation is an intensely studied quantum phenomenon that emerges at low temperatures. While preceding Bose–Einstein condensation models do not consider what statistics apply above the condensation temperature, we show that neglecting this question leads to inconsistencies. A mathematically rigorous calculation of Bose–Einstein condensation temperature requires evaluating the thermodynamic balance between coherent and incoherent particle populations. The first part of this work develops such an improved Bose–Einstein condensation temperature calculation, for both three-dimensional and two-dimensional scenarios. The progress over preceding Bose–Einstein condensation models is particularly apparent in the two-dimensional case, where preceding models run into mathematical divergence. In the Discussion section, we compare our mathematical model against experimental superconductivity data. A remarkable match is found between experimental data and the calculated Bose–Einstein condensation temperature formulas. Our mathematical model therefore appears applicable to superconductivity, and may facilitate a rational search for higher-temperature superconductors. Full article

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13 pages, 3438 KB

Open AccessArticle

Three-Dimensional Modelling and Validation for the Ultra-High-Speed EDS Rocket Sled with PM Halbach Array

by Yongpan Hu, Baojun Chen, Guobin Lin and Zhiqiang Wang

Actuators 2025, 14(5), 225; https://doi.org/10.3390/act14050225 - 1 May 2025

Viewed by 772

Abstract

The ultra-high-speed rocket sled plays an important role in the ground test by simulating altitude flight. Rocket sleds can only be lifted for a short time with thermally uninsulated superconductors moving among an eddy-current-induced copper array. For the purpose of durable lifting, an [...] Read more.

The ultra-high-speed rocket sled plays an important role in the ground test by simulating altitude flight. Rocket sleds can only be lifted for a short time with thermally uninsulated superconductors moving among an eddy-current-induced copper array. For the purpose of durable lifting, an electrodynamic suspension (EDS) with a permanent magnet (PM) Halbach array moving over a conductor plate can be adopted to upgrade the rocket sled. The earlier study built a two-dimensional (2D) model for the PM EDS system. Yet, 2D modelling in our earlier research ignored the magnetic field variation along both widths of the Halbach array and conductor plate. This resulted in a more than 50% error between the analytical electromagnetic forces with both the three-dimensional (3D) simulated and experimental results. To reduce the error, this paper puts forward more accurate analytical electromagnetic force formulas by a 3D modelling method encompassing both widths of the Halbach array and conductor plate. The 3D model was built by periodically extending the PM EDS system along both directions of the width and length. Then, by double Fourier series expansion and omitting high-order components, the electromagnetic forces can be approximated by brief formulas. Moreover, lift-to-weight and lift-to-drag optimization are discussed. Finally, the correctness of the 3D electromagnetic force formulas was verified by both the numerical simulation and experiment. Full article

(This article belongs to the Special Issue Advanced Theory and Application of Magnetic Actuators—2nd Edition)

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10 pages, 1251 KB

Open AccessCommunication

Engineering Terahertz Light–Matter Interaction with Quantum Electronic Metamaterials

by Igor I. Smolyaninov and Vera N. Smolyaninova

Electronics 2025, 14(4), 679; https://doi.org/10.3390/electronics14040679 - 10 Feb 2025

Viewed by 1144

Abstract

While electromagnetic metamaterials completely revolutionized optics and radio frequency engineering, recent progress in the development of conceptually related electronic metamaterials was more slow. Similar to electromagnetic metamaterials, which engineer material response to the electromagnetic field of a photon, the purpose of electronic metamaterials [...] Read more.

While electromagnetic metamaterials completely revolutionized optics and radio frequency engineering, recent progress in the development of conceptually related electronic metamaterials was more slow. Similar to electromagnetic metamaterials, which engineer material response to the electromagnetic field of a photon, the purpose of electronic metamaterials is to affect electron propagation and its wave function by changing material response to its electric field. This makes electronic metamaterials an ideal tool for engineering light–matter interaction in semiconductors and superconductors. Here, we propose the use of Fermi’s quantum refraction, which was previously observed in the terahertz spectroscopy of Rydberg atoms and two-dimensional surface electronic states, as a novel tool in quantum electronic metamaterial design. In particular, we demonstrate several potential applications of this concept in two-dimensional metamaterial superconductors and “universal quantum dots” designed for operation in the terahertz frequency range. Full article

(This article belongs to the Special Issue Terahertz Optics and Spectroscopy)

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13 pages, 1122 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Simple Model for T_c and Pairing Symmetry Changes in Sr₂RuO₄ Under (100) Uniaxial Strain

by Macauley Curtis, Martin Gradhand and James F. Annett

Condens. Matter 2024, 9(4), 44; https://doi.org/10.3390/condmat9040044 - 1 Nov 2024

Viewed by 3057

Abstract

Uniaxial strain in the (100) direction has the effect of increasing the superconducting

T_{c}

in Sr₂RuO₄ from

1.5

K to over 3 K. The enhanced

T_{c}

corresponds to a Lifshitz transition in the Fermi surface topology of this [...] Read more.

Uniaxial strain in the (100) direction has the effect of increasing the superconducting

T_{c}

in Sr₂RuO₄ from

1.5

K to over 3 K. The enhanced

T_{c}

corresponds to a Lifshitz transition in the Fermi surface topology of this unconventional superconductor. We model this using a simple two-dimensional one-band model for the

γ

sheet of the Fermi surface. This reproduces the experimental

T_{c}

results well if we assume a

d_{x^{2} - y^{2}}

singlet pairing state. On the other hand, the triplet state

p_{x} + i p_{y}

does not show any distinct peaks in

T_{c}

associated with the Lifshitz transition. A mixed symmetry state pairing of the form

d + i g

can both describe the

T_{c}

changes and show a distinct transition temperature for time-reversal symmetry breaking (TRSB). Full article

(This article belongs to the Special Issue Superstripes Physics, 3rd Edition)

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11 pages, 452 KB

Open AccessArticle

Stable Majorana Zero-Energy Modes in Two-Dimensional Josephson Junctions

by Yuting Huang, Qinyi Wang, Lei Li and Zhenying Wen

Symmetry 2024, 16(8), 1066; https://doi.org/10.3390/sym16081066 - 19 Aug 2024

Cited by 1 | Viewed by 2123

Abstract

In this paper, a modified Josephson junction model is proposed, which splits the two-dimensional electron gas by inserting a middle superconductor strip into a conventional Josephson junction. This modification enhances the superconducting proximity effect, thus avoiding the appearance of a soft gap and [...] Read more.

In this paper, a modified Josephson junction model is proposed, which splits the two-dimensional electron gas by inserting a middle superconductor strip into a conventional Josephson junction. This modification enhances the superconducting proximity effect, thus avoiding the appearance of a soft gap and inducing a stable Majorana zero-energy mode. Through numerical simulation, the impact of the middle superconductor strip with different widths on the energy band structure is studied, and a significant increase in the topological energy gap is found. In addition, the modified system maintains a robust topological gap even at a strong in-plane magnetic field. Full article

(This article belongs to the Section Physics)

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11 pages, 3212 KB

Open AccessArticle

Superhard and Superconducting Bilayer Borophene

by Chengyong Zhong, Minglei Sun, Tariq Altalhi and Boris I. Yakobson

Materials 2024, 17(9), 1967; https://doi.org/10.3390/ma17091967 - 24 Apr 2024

Cited by 46 | Viewed by 3036

Abstract

Two-dimensional superconductors, especially the covalent metals such as borophene, have received significant attention due to their new fundamental physics, as well as potential applications. Furthermore, the bilayer borophene has recently ignited interest due to its high stability and versatile properties. Here, the mechanical [...] Read more.

Two-dimensional superconductors, especially the covalent metals such as borophene, have received significant attention due to their new fundamental physics, as well as potential applications. Furthermore, the bilayer borophene has recently ignited interest due to its high stability and versatile properties. Here, the mechanical and superconducting properties of bilayer-

δ_{6}

borophene are explored by means of first-principles computations and anisotropic Migdal–Eliashberg analytics. We find that the coexistence of strong covalent bonds and delocalized metallic bonds endows this structure with remarkable mechanical properties (maximum 2D-Young’s modulus of ~570 N/m) and superconductivity with a critical temperature of ~20 K. Moreover, the superconducting critical temperature of this structure can be further boosted to ~46 K by applied strain, which is the highest value known among all borophenes or two-dimensional elemental materials. Full article

(This article belongs to the Special Issue Development of Boron-Based Materials)

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27 pages, 10252 KB

Open AccessReview

Metal Chalcogenide–Hydroxide Hybrids as an Emerging Family of Two-Dimensional Heterolayered Materials: An Early Review

by Yuri Mikhlin, Maxim Likhatski, Roman Borisov, Denis Karpov and Sergey Vorobyev

Materials 2023, 16(19), 6381; https://doi.org/10.3390/ma16196381 - 24 Sep 2023

Cited by 10 | Viewed by 2552

Abstract

Two-dimensional (2D) materials and phenomena attract huge attention in modern science. Herein, we introduce a family of layered materials inspired by the minerals valleriite and tochilinite, which are composed of alternating “incompatible”, and often incommensurate, quasi-atomic sheets of transition metal chalcogenide (sulfides and [...] Read more.

Two-dimensional (2D) materials and phenomena attract huge attention in modern science. Herein, we introduce a family of layered materials inspired by the minerals valleriite and tochilinite, which are composed of alternating “incompatible”, and often incommensurate, quasi-atomic sheets of transition metal chalcogenide (sulfides and selenides of Fe, Fe-Cu and other metals) and hydroxide of Mg, Al, Fe, Li, etc., stacked via electrostatic interaction rather than van der Waals forces. We survey the data available on the composition and structure of the layered minerals, laboratory syntheses of such materials and the effect of reaction conditions on the phase purity, morphology and composition of the products. The spectroscopic results (Mössbauer, X-ray photoelectron, X-ray absorption, Raman, UV-vis, etc.), physical (electron, magnetic, optical and some others) characteristics, a specificity of thermal behavior of the materials are discussed. The family of superconductors (FeSe)·(Li,Fe)(OH) having a similar layered structure is briefly considered too. Finally, promising research directions and applications of the valleriite-type substances as a new class of prospective multifunctional 2D materials are outlined. Full article

(This article belongs to the Special Issue Two-Dimensional Materials and Nano Devices)

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14 pages, 7156 KB

Open AccessArticle

Mechanical Analysis and Testing of Conduction-Cooled Superconducting Magnet for Levitation Force Measurement Application

by Liyuan Liu, Wei Chen, Huimin Zhuang, Fei Chi, Gang Wang, Gexiang Zhang, Jing Jiang, Xinsheng Yang and Yong Zhao

Crystals 2023, 13(7), 1117; https://doi.org/10.3390/cryst13071117 - 17 Jul 2023

Cited by 1 | Viewed by 2963

Abstract

High-temperature superconductors have great potential for various engineering applications such as a flywheel energy storage system. The levitation force of bulk YBCO superconductors can be drastically increased by increasing the strength of the external field. Therefore, a 6T conduction-cooled superconducting magnet has been [...] Read more.

High-temperature superconductors have great potential for various engineering applications such as a flywheel energy storage system. The levitation force of bulk YBCO superconductors can be drastically increased by increasing the strength of the external field. Therefore, a 6T conduction-cooled superconducting magnet has been developed for levitation force measurement application. Firstly, to protect the magnet from mechanical damage, reliable stress analysis inside the coil is paramount before the magnet is built and tested. Therefore, a 1/4 two-dimensional (2D) axisymmetric model of the magnet was established, and the mechanical stress in the whole process of winding, cooling down and energizing of the magnet was calculated. Then, the charging, discharging, and preliminary levitation force performance tests were performed to validate the operating stability of the magnet. According to the simulation results, the peak stresses of all coil models are within the allowable value and the winding maintains excellent mechanical stability in the superconducting magnet. The test results show that the superconducting magnet can be charged to its desired current of 150 A without quenching and maintain stable operation during the charging and discharging process. What is more, the superconducting magnet can meet the requirements for the levitation force measurement of both low magnetic field and high magnetic field. Full article

(This article belongs to the Special Issue Research on High-Temperature Superconducting Materials)

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16 pages, 1086 KB

Open AccessEditor’s ChoiceArticle

On the Size of Superconducting Islands on the Density-Wave Background in Organic Metals

by Vladislav D. Kochev, Seidali S. Seidov and Pavel D. Grigoriev

Magnetochemistry 2023, 9(7), 173; https://doi.org/10.3390/magnetochemistry9070173 - 4 Jul 2023

Cited by 4 | Viewed by 2115

Abstract

Most high-

T_{c}

superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, [...] Read more.

Most high-

T_{c}

superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure

P_{c}

, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg–Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)

_{2}

PF

_{6}

samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors. Full article

(This article belongs to the Special Issue Functional Molecular Materials Insights—a Themed Issue in Honour of Professor Manuel Almeida on the Occasion of His 70th Birthday)

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18 pages, 482 KB

Open AccessFeature PaperArticle

Charge-Density Waves vs. Superconductivity: Some Results and Future Perspectives

by Giulia Venditti and Sergio Caprara

Condens. Matter 2023, 8(3), 54; https://doi.org/10.3390/condmat8030054 - 27 Jun 2023

Cited by 7 | Viewed by 5619

Abstract

Increasing experimental evidence suggests the occurrence of filamentary superconductivity in different (quasi) two-dimensional physical systems. In this piece of work, we discuss the proposal that under certain circumstances, this occurrence may be related to the competition with a phase characterized by charge ordering [...] Read more.

Increasing experimental evidence suggests the occurrence of filamentary superconductivity in different (quasi) two-dimensional physical systems. In this piece of work, we discuss the proposal that under certain circumstances, this occurrence may be related to the competition with a phase characterized by charge ordering in the form of charge-density waves. We provide a brief summary of experimental evidence supporting our argument in two paradigmatic classes of materials, namely transition metal dichalcogenides and cuprates superconductors. We present a simple Ginzburg–Landau two-order-parameters model as a starting point to address the study of such competition. We finally discuss the outcomes of a more sophisticated model, already presented in the literature and encoding the presence of impurities, and how it can be further improved in order to really address the interplay between charge-density waves and superconductivity and the possible occurrence of filamentary superconductivity at the domain walls between different charge-ordered regions. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors VII)

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18 pages, 3123 KB

Open AccessArticle

Contribution of Processes in SN Electrodes to the Transport Properties of SN-N-NS Josephson Junctions

by Vsevolod Ruzhickiy, Sergey Bakurskiy, Mikhail Kupriyanov, Nikolay Klenov, Igor Soloviev, Vasily Stolyarov and Alexander Golubov

Nanomaterials 2023, 13(12), 1873; https://doi.org/10.3390/nano13121873 - 16 Jun 2023

Cited by 13 | Viewed by 2587

Abstract

In this paper, we present a theoretical study of electronic transport in planar Josephson Superconductor–Normal Metal–Superconductor (SN-N-NS) bridges with arbitrary transparency of the SN interfaces. We formulate and solve the two-dimensional problem of finding the spatial distribution of the supercurrent in the SN [...] Read more.

In this paper, we present a theoretical study of electronic transport in planar Josephson Superconductor–Normal Metal–Superconductor (SN-N-NS) bridges with arbitrary transparency of the SN interfaces. We formulate and solve the two-dimensional problem of finding the spatial distribution of the supercurrent in the SN electrodes. This allows us to determine the scale of the weak coupling region in the SN-N-NS bridges, i.e., to describe this structure as a serial connection between the Josephson contact and the linear inductance of the current-carrying electrodes. We show that the presence of a two-dimensional spatial current distribution in the SN electrodes leads to a modification of the current–phase relation and the critical current magnitude of the bridges. In particular, the critical current decreases as the overlap area of the SN parts of the electrodes decreases. We show that this is accompanied by a transformation of the SN-N-NS structure from an SNS-type weak link to a double-barrier SINIS contact. In addition, we find the range of interface transparency in order to optimise device performance. The features we have discovered should have a significant impact on the operation of small-scale superconducting electronic devices, and should be taken into account in their design. Full article

(This article belongs to the Special Issue Nanostructures for Superconducting Electronics)

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21 pages, 3693 KB

Open AccessArticle

Intrinsic Coherence Length Anisotropy in Nickelates and Some Iron-Based Superconductors

by Evgeny F. Talantsev

Materials 2023, 16(12), 4367; https://doi.org/10.3390/ma16124367 - 13 Jun 2023

Cited by 2 | Viewed by 2732

Abstract

Nickelate superconductors, R_1−xA_xNiO₂ (where R is a rare earth metal and A = Sr, Ca), experimentally discovered in 2019, exhibit many unexplained mysteries, such as the existence of a superconducting state with T_c (up to 18 K) [...] Read more.

Nickelate superconductors, R_1−xA_xNiO₂ (where R is a rare earth metal and A = Sr, Ca), experimentally discovered in 2019, exhibit many unexplained mysteries, such as the existence of a superconducting state with T_c (up to 18 K) in thin films and yet absent in bulk materials. Another unexplained mystery of nickelates is their temperature-dependent upper critical field,

B_{c 2} (T)

, which can be nicely fitted to two-dimensional (2D) models; however, the deduced film thickness,

d_{s c, G L}

, exceeds the physical film thickness,

d_{s c}

, by a manifold. To address the latter, it should be noted that 2D models assume that

d_{s c}

is less than the in-plane and out-of-plane ground-state coherence lengths,

d_{s c} < ξ_{a b} (0)

and

d_{s c} < ξ_{c} (0)

, respectively, and, in addition, that the inequality

ξ_{c} (0) < ξ_{a b} (0)

satisfies. Analysis of the reported experimental

B_{c 2} (T)

data showed that at least one of these conditions does not satisfy for R_1-xA_xNiO₂ films. This implies that nickelate films are not 2D superconductors, despite the superconducting state being observed only in thin films. Based on this, here we propose an analytical three-dimensional (3D) model for a global data fit of in-plane and out-of-plane

B_{c 2} (T)

in nickelates. The model is based on a heuristic expression for temperature-dependent coherence length anisotropy:

γ_{ξ} (T) = \frac{γ_{ξ} (0)}{1 - \frac{1}{a} \times \frac{T}{T_{c}}}

, where

a > 1

is a unitless free-fitting parameter. The proposed expression for

γ_{ξ} (T)

, perhaps, has a much broader application because it has been successfully applied to bulk pnictide and chalcogenide superconductors. Full article

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