An Explanation of the Temperature-Dependent Upper Critical Field Data of H3S on the Basis of the Thermodynamics of a Superconductor in a Magnetic Field

Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (Hc2) of H3S (critical temperature, Tc ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtained by Talantsev (2019) in an approach based on an ingenious mix of the Ginzberg-Landau (GL), the Werthamer, Helfand and Hohenberg (WHH), and the Gor’kov, etc., theories which have individually been employed for the same purpose for a long time. Up to the lowest temperature (TL) in each of these data-sets, similarly accurate fits have also been obtained by Malik and Varma (2023) in a radically different approach based on the Bethe-Salpeter equation (BSE) supplemented by the Matsubara and the Landau quantization prescriptions. For T TL, however, while the (GL, WHH, etc.)-based approach leads to Hc2(0) ≈ 100 T, the BSE-based approach leads to about twice this value even at 1 K. In this paper, a fit to one of the said data-sets is obtained for the first time via a thermodynamic approach which, up to TL, is as good as those obtained via the earlier approaches. While this is interesting per se, another significant result of this paper is that for T TL it corroborates the result of the BSE-based approach.

A Dynamical Approach to the Explanation of the Upper Critical Field Data of Compressed H3S

Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (Hc2(T)) data of H3S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S1 = {Tc, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of Hc2(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for Hc2(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of Hc2(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S2 = {μ, m*, interaction parameter λm, Landau index NL}, which is altogether different from S1.

The upper critical field in two-band layered superconductors

The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau （GL） theory. The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad temperature range. Based on the GL theory for clean superconductors, a phenomenological theory for dirty superconductor is proposed. Selecting appropriate parameters, two-band layered GL theory is successfully applied to the crystal of Mg（B1-xCx）2 and the neutron irradiation samples of MgB2.

Superconductivity with peculiar upper critical fields in quasi-one-dimensional Cr-based pnictides

The discovery of superconductivity in quasi-one-dimensional Cr-based pnictides A2Cr3As3（A = alkali metals） has generated considerable research interest, primarily owing to their reduced dimensionality, significant electron correlations,and possible unconventional superconductivity. The upper critical field（Hc2） provides important information on the superconducting pairing. In this paper, we first briefly overview the latest research progress on the Cr-based superconductors.Then, we introduce typical Hc2（T） behaviors of type-II superconductors in relation with the pair-breaking mechanisms.After a description of the measurement method for Hc2, we focus on the analysis of Hc2 data, especially for the temperature and angle dependence, in K2Cr3As3 crystals. The result indicates（i） an absence of Pauli-paramagnetic pair breaking for field perpendicular to the Cr3As3 chains, and（ii） a unique threefold modulation for the in-plane Hc2Φ profile. Finally we conclude with remarks on the possible unconventional superconducting pairing symmetry.

Investigation of dimensionality in superconducting NbN thin film samples with different thicknesses and NbTiN meander nanowire samples by measuring the upper critical field

We study superconducting properties of NbN thin film samples with different thicknesses and an ultra-thin NbTiN meander nanowire sample.For the ultra-thin samples,we found that the temperature dependence of upper critical field(Hc2)in parallel to surface orientation shows bending curvature close to critical temperature Tc,suggesting a two-dimensional(2D)nature of the samples.The 2D behavior is further supported by the angular dependence measurements of Hc2 for the thinnest samples.The temperature dependence of parallel upper critical field for the thick films could be described by a model based on the anisotropic Ginzburg-Landau theory.Interestingly,the results measured in the field perpendicular to the film surface orientation show a similar bending curvature but in a much narrow temperature region close to Tc for the ultra-thin samples.We suggest that this feature could be due to suppression of pair-breaking caused by local in-homogeneity.We further propose the temperature dependence of perpendicular Hc2 as a measure of uniformity of superconducting ultra-thin films.For the thick samples,we find that Hc2 shows maxima for both parallel and perpendicular orientations.The Hc2 peak for the perpendicular orientation is believed to be due to the columnar structure formed during the growth of the thick films.The presence of columnar structure is confirmed by transmission electron microscopy(TEM).In addition,we have measured the angular dependence of magneto-resistance,and the results are consistent with the Hc2 data.

Different behavior of upper critical field in Fe1-xSe single crystals

The temperature dependences of upper critical field(Hc2) for a series of iron-deficient Fe1-xSe single crystals are obtained from the measurements of in-plane resistivity in magnetic fields up to 9 T and perpendicular to the ab plane. For the samples with lower superconducting transition temperature Tc(< 7.2 K), the temperature dependence of Hc2 is appropriately described by an effective two-band model. For the samples with higher Tc( 7.2 K), the temperature dependence can also be fitted by a single-band Werthamer–Helfand–Hohenberg formula, besides the two-band model. Such a Tc-dependent change in Hc2(T) behavior is discussed in connection with recent related experimental results, showing an inherent link between the changes of intrinsic superconducting and normal state properties in the Fe Se system.

Anisotropy of Critical Fields in MgB_2: Two-Band Ginzburg-Landau Theory for Layered Superconductors

The temperature dependence of the anisotropy parameter of upper critical field γHe2 （T） = Hc2^‖ （T） /Hc2^⊥ （T） and London penetration depth γλ （T） = λ‖（T）/λ⊥ （T） are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 （T） is increased, while the London penetration depth anisotropy γλ（T） reveals an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations..Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.

Planckian dissipation and non-Ginzburg-Landau type upper critical field in Bi2201

Resistivity and Hall effect measurements have been carried out on a micro-fabricated bridge of Bi2201 single crystal at low temperatures down to 0.4 K under high magnetic fields.When superconductivity is crashed by a high magnetic field,the recovered "normal state" resistivity still shows a linear temperature dependence in the low temperature region.Combining with the effective mass and the charge carrier density,we get a linear scattering rate 1/τ=αkBT/h with 0.77 <α <1.16,which gives a strong evidence of the Planckian dissipation.Furthermore,our results reveal a new type of temperature dependence of the upper critical field,H_(c2)(T)=H*■,which is totally different from the expectation of the Ginzburg-Landau theory,and suggests the existence of uncondensed Cooper pairs above H_(c2)(T) line.

Strong Pauli paramagnetic effect in the upper critical field of KCa2Fe4As4F2

Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-Fe As-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, Tc, in KCa2Fe4As4F2 single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane(H∥c, Hc2c) and in-plane(H∥ab, Hc2ab ) directions have been measured.A sublinear temperature-dependent behavior is observed for the out-of-plane Hc2c , whereas strong convex curvature with cooling is observed for the in-plane Hc2ab . Such behaviors could not be described by the conventional Werthamer-Helfand-Hohenberg(WHH) model. The data analysis based on the WHH model by considering the spin aspects reveals a large Maki parameter α=9,indicating that the in-plane upper critical field is affected by a very strong Pauli paramagnetic effect.

ESTIMATE OF THE UPPER CRITICAL FIELD AND CONCENTRATION FOR SUPERCONDUCTOR

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the upper critical magnetic field Hc3 at which superconductivity can nucleate is estimated. In addition, the authors locate the concentration of the order parameter, which depends on the inhomogeneous term a(x). Unlikely to the homogeneous case, the order parameter may concentrate in the interior of the superconducting material, due to the influence of the inhomogeneous term a(x).

Universal behavior of the upper critical field in iron-based superconductors

The newly discovered iron-based high temperature superconductors have demonstrated rich phys- ical properties. Here we give a brief review on the recent studies of the upper critical field and its anisotropy in a few typical series of the iron-based superconductors （FeSCs）. In spite of their characters of a layered crystal structure, all the FeSCs possess an extremely large upper critical field and a weak anisotropy of superconductivity, being unique among the layered superconductors. These particular properties indicate potential applications of the FeSCs in the future. Based on the experimental facts of the FeSCs, we will discuss the possible mechanisms of pair breaking in high magnetic fields and its restrictions on the theoretical analysis of the superconducting pairing mechanisms.

Studies on the characteristics of Barkhausen emission and evaluation of the critical fields for domain wall notion in nickel

Acoustic Barkhausen Emission (ABE) and Electromagnetic Barkhausen Emission (EBE) have been measured. Explanations of the response of nickel to an applied magnetic field are considered using energy density diagrams and critical fields deduced using Kersten's modified theory. These theoretical models are correlated with ABE and EBE measurements, providing further confirmation of the origins of ABE being non-180° domain wall motion. This paper also shows that the motion of domain walls, on increasing the magnetising fields from saturation to satu -ration, follows the sequence of 71°-180° - 109°. Values of critical fields correponding to 71°, 180° and 109° wall motions in nickel are determined using these techniques .

A New Approach to the Determination of the Critical Slip Surfaces of Slopes

A new method for the determination of the critical slip surfaces of slopes is proposed in this paper. In this paper, the original critical slip field method is extended in terms of the total residual moment, values of residual work as well as the unbalanced thrust force at the exit point for a given non-circular slip surface. The most critical slip surface with the maximum representative value for a prescribed factor of safety will be optimized and located using the harmony search algorithm. The prescribed factor of safety is modified with certain tiny interval in order to find the critical slip surface where the maximum representative value is zero. The aforementioned approach to the location of the critical slip surface is greatly different from the traditional limit equilibrium procedure. Three typical soil slopes are evaluated by use of the proposed method, and the comparisons with the classical approaches have illustrated the applicability of the proposed method.

Drift effect on vacuum birefringence in a strong electric and magnetic field

As an important QED effect to detect the vacuum polarization, birefringence in the presence of a strong electric and magnetic field, E0⊥ B0, E0≤ c B0, is considered. The directional dependence of birefringence is obtained. In two special cases： E0= 0 and E0= c B0, our results are consistent with the previous ones. The refractive index of the probe wave propagating in the -E0× B0 direction decreases with E0/c B0, while that in the-E0× B0 direction increases with E0/c B0.The physics of the direction dependence of birefringence maybe the E0× B0 drift velocity of the virtual electrons and positrons.

Compressed H3S: Fits to the Empirical Hc2(T) Data and a Discussion of the Meissner Effect

Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field Hc2(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical Hc2(T) data of H3S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H3S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H3S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs Ns at T = Tc) should shed new light on the issue being addressed.

Synthesis of large FeSe superconductor crystals via ion release/introduction and property characterization

Large superconducting Fe Se crystals of（001） orientation have been prepared via a hydrothermal ion release/introduction route for the first time. The hydrothermally derived Fe Se crystals are up to 10 mm×5 mm×0.3 mm in dimension. The pure tetragonal FeSe phase has been confirmed by x-ray diffraction（XRD） and the composition determined by both inductively coupled plasma atomic emission spectroscopy（ICP-AES） and energy dispersive x-ray spectroscopy（EDX）. The superconducting transition of the Fe Se samples has been characterized by magnetic and transport measurements. The zero-temperature upper critical field H（c2） is calculated to be 13.2–16.7 T from a two-band model. The normal-state cooperative paramagnetism is found to be predominated by strong spin frustrations below the characteristic temperature T（sn）, where the Ising spin nematicity has been discerned in the FeSe superconductor crystals as reported elsewhere.

Fabrication and properties of the meander nanowires based on ultra-thin Nb films

We report the fabrication and the study of superconducting properties of ultra-thin Nb superconducting meander nanowires, which can be used as superconducting nanowire single-photon detectors （SNSPDs）. The ultra-thin （about 7- nm thick） Nb films are patterned into micro-bridges, and 100-nm wide meander nanowires by using e-beam lithography （EBL）. The average transition temperature （Tc） of the nanowires is about 4.8 K and the critical current density jc is about 2.8 × 10^6 A/cm2. Superconducting characteristics of the specimens at different applied magnetic fields up to 8 T （parallel or perpendicular to the specimen） are systematically investigated. The normalized temperature t （= T/Tc） dependences of the parallel critical field （HcⅡ） for both the micro-bridge and the meander nanowire are almost the same, following the Ginzburg and Landau （GL） formalism for ultra-thin films. However, in perpendicular field and in the vicinity of Tc （〉 0.95Tc）, the critical field Hc⊥ of the nanowire exhibits a down-turn curvature nonlinear temperature dependence while the micro-bridge displays a linear temperature dependence. The nonlinear behavior of Hc⊥ in the nanowire is believed to be due to the fact that in the vicinity of Tc the coherence length becomes larger than the line width. Additionally, the localization of carriers in the nanowire could also contribute to the nonlinear behavior. The resistive transitions could be described by the phase-slip model for quasi-one-dimensional system. Moreover, the hysteresis in I-V curve of the meander nanowires can be illustrated by a simple model of localized normal hotspot maintained by Joule heating.

A new analytical model of high voltage silicon on insulator(SOI) thin film devices

A new analytical model of high voltage silicon on insulator （SOI） thin film devices is proposed, and a formula of silicon critical electric field is derived as a function of silicon film thickness by solving a 2D Poisson equation from an effective ionization rate, with a threshold energy taken into account for electron multiplying. Unlike a conventional silicon critical electric field that is constant and independent of silicon film thickness, the proposed silicon critical electric field increases sharply with silicon fihn thickness decreasing especially in the case of thin films, and can come to 141V/μm at a film thickness of 0.1 μm which is much larger than the normal value of about 30 V/μm. From the proposed formula of silicon critical electric field, the expressions of dielectric layer electric field and vertical breakdown voltage （VB,V） are obtained. Based on the model, an ultra thin film can be used to enhance dielectric layer electric field and so increase vertical breakdown voltage for SOI devices because of its high silicon critical electric field, and with a dielectric layer thickness of 2 μm the vertical breakdown voltages reach 852 and 300V for the silicon film thicknesses of 0.1 and 5μm, respectively. In addition, a relation between dielectric layer thickness and silicon film thickness is obtained, indicating a minimum vertical breakdown voltage that should be avoided when an SOI device is designed. 2D simulated results and some experimental results are in good agreement with analytical results.

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.

A THEORETICAL MODEL OF MAGNETOELASTIC BUCKLING FOR SOFT FERROMAGNETIC THIN PLATES

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.