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.

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume-Capel model （BCM） in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.

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.

An Integrated Study of ULF Magnetic Field Variations in Association with the 2008 Sichuan Earthquake, on the Basis of Statistical and Critical Analyses

The ultra-low frequency (ULF) magnetic field data at a station very close to the 2008 Sichuan earthquake (EQ) (on 12 May, 2008;M = 8.0) are extensively studied on the basis of combined statistical and natural time analyses. Two effects in ULF are treated: one is the well-known ULF radiation from the lithosphere, and the other is the non-conventional depression of ULF horizontal magnetic field. The simple statistical analysis has yielded: 1) no clear evidence of the presence of precursory ULF radiation, and 2) a significant effect of depression of ULF horizontal field a few days before the EQ (as a signature of ionospheric perturbations). The recently introduced natural time analysis has also been performed in order to study the critical features of the lithosphere and essentially new information has been brought about. The parameter “polarization”, as the ratio of vertical to horizontal components, showed critical features in the time period of 17 - 27 April, about one month to two weeks before the EQ as a signature of lithospheric radiation. Then, the natural time analysis has reconfirmed the presence of ionospheric perturbations a few days before the EQ, together with an additional time window found on 19 - 23 April, about one month before the EQ, exhibiting critical features in the ULF depression.

A Fermi Energy-Incorporated Framework for Dealing with the Temperature- and Magnetic Field-Dependent Critical Current Densities of Superconductors and Its Application to Bi-2212

It is well known that the critical current density of a superconductor depends on its size, shape, nature of doping and the manner of preparation. It is suggested here that the collective effect of such differences for different samples of the same superconductor is to endow them with different values of the Fermi energy—a single property to which may be attributed the observed variation in their critical current densities. The study reported here extends our earlier work concerned with the generalized BCS equations [Malik, G.P. (2010) Physica B, 405, 3475-3481;Malik, G.P. (2013) WJCMP, 3,103-110]. We develop here for the first time a framework of microscopic equations that incorporates all of the following parameters of a superconductor: temperature, momentum of Cooper pairs, Fermi energy, applied magnetic field and critical current density. As an application of this framework, we address the different values of critical current densities of Bi-2212 for non-zero values of temperature and applied magnetic field that have been reported in the literature.

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.

Numerical Calculation of Geoelectric Fields That Affect Critical Infrastructure

One of the modern applications of geomagnetism is determining the effect of geomagnetic disturbances on critical infrastructure such as power systems and pipelines. Assessing the geomagnetic hazard to such systems requires calculation of the geoelectric fields produced during geomagnetic disturbances. Such geoelectric fields can then be used as input to system models to calculate the impact on the system. This paper describes what is involved in calculating the geoelectric fields produced during real geomagnetic disturbances. The theory of geomagnetic induction is presented and used to derive the Earth transfer function relating the geoelectric and geomagnetic field variations at the Earth’s surface. It is then shown how this can be used to make practical calculations of the geoelectric fields and how the calculation process can be verified by comparison with analytic solutions obtained with synthetic geomagnetic variation data. The accuracy of the calculated geoelectric fields for geomagnetic risk assessments is limited, not by the accuracy of the calculation methods, but by the availability of geomagnetic field measurements and Earth conductivity information over the whole extent of the affected infrastructure.

Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing:A numerical investigation

By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopoten- tials （PPs） without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall （FQH） states both in the lowest Landau level （LLL） and first excited Landau level （1LL）. The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values, while the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.

Phase diagram and collective modes in Rashba spin–orbit coupled BEC: Effect of in-plane magnetic field

We studied the system of pure Rashba spin–orbit coupled Bose gas with an in-plane magnetic field. Based on the mean field theory, we obtained the zero temperature phase diagram of the system which exhibits three phases, plane wave（PW） phase, striped wave（SW） phase, and zero momentum（ZM） phase. It was shown that with a growing in-plane field,both SW and ZM phases will eventually turn into the PW phase. Furthermore, we adopted the Bogoliubov theory to study the excitation spectrum as well as the sound speed.

Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions

The influence of the chiral mean field on the in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization, which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the in-plane flow.

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.

Critical Properties of Mixed Ising Spin System with Different Trimodal Transverse Fields in the Presence of Single-Ion Anisotropy

Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-lon anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T-Ω1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T-Ω1 space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T-D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.

Influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a Rashba two-dimensional electron gas

We study theoretically the influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a two-dimensional electron gas with Rashba spin-orbit coupling. We show that, after such an influence is taken into account, the static intrinsic spin-Hall effect can be stabilized in a disordered Rashba twodimensional electron gas, and the static intrinsic spin-Hall conductivity shall exhibit some interesting characteristics as conceived in some original theoretical proposals.

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.

Study of Upper Critical Magnetic Field of Superconducting HoMo₆Se₈

This work focuses on the study of mathematical aspects of upper critical magnetic field of superconducting HoMo6Se8. At zero external magnetic field, HoMo6Se8 was found to undergo a transition from the normal state to the superconducting state at 5.6 K and returned to a normal but magnetically ordered state between the temperature range of 0.3 K and 0.53 K. The main objective of this work is to show the temperature dependence of the upper critical magnetic field of superconducting HoMo6Se8 by using the Ginzburg-Landau (GL) phenomenological Equation. We found the direct relationship between the GL coherence length (ξGL) and penetration depth (λGL) with temperature. From the GL Equations and the results obtained for the GL coherence length, the expression for upper critical magnetic field (Hc2) is obtained for the superconducting HoMo6Se8. The result is plotted as a function of temperature. The graph shows the linear dependence of upper critical magnetic field (Hc2) with temperature (T) and our finding is in agreement with experimental observations.

On a Heuristic Point of View about the Generalization of Curie Law to Cosmic Higgs Fields with the Casimir Effect

Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform into paramagnetic substances. Below the Curie temperature, a material remains ferromagnetic;above it, the material becomes paramagnetic, with its magnetic field easily influenced by external magnetic fileds. For example, the Curie temperature of iron (Fe) is 1043 K, while that of neodymium magnets ranges from 583 to 673 K. From both physics and mathematics perspectives, examining the temperature properties of materials is essential, as it provides valuable insights into their electromagnetic and thermodynamic behaviors. This paper makes a bold assumption and, for the first time, carefully verifies the existence of a Casimir temperature at 0.00206 K under conditions of one-atomic spacing.

CRITICAL BEHAVIOR OF S -3/2 ISING MODEL IN RANDOM LONGITUDINAL AND TRANSVERSE FIELDS

The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).

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.