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.

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.

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.

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.

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.

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.

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.

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.

Enhancement of Ising superconductivity in monolayer NbSe_(2) via surface fluorination

Recently discovered Ising superconductors have garnered considerable interest due to their anomalously large in-plane upper critical fields(B_(c2)). However, the requisite strong spin-orbital coupling in the Ising pairing mechanism generally renders these superconductors heavy-element dominant with notably low superconducting transition temperatures(Tc). Here, based on the Migdal-Eliashberg theory and the mean-field Bogoliubov-de Gennes Hamiltonian, we demonstrate a significant enhancement of Ising superconductivity in monolayer NbSe_(2) through surface fluorination, as evidenced by concomitant improvements in Tcand Bc_(2). This enhancement arises from three predominant factors. Firstly, fluorine atoms symmetrically and stably adhere to both sides of the monolayer NbSe_(2), thereby maintaining the out-of-plane mirror symmetry and locking carrier spins out-of-plane.Secondly, fluorination suppresses the charge density wave in monolayer NbSe_(2) and induces a van Hove singularity in the vicinity of the Fermi level, leading to a marked increase in the number of carriers and, consequently, strengthening the electron-phonon coupling(EPC). Lastly, the appearance of fluorine-related, low-frequency phonon modes further augments the EPC. Our findings suggest a promising avenue to elevate Tcin two-dimensional Ising superconductors without compromising their Ising pairing.

Enhanced superconductivity in hole-doped Nb2PdS5

We synthesized a series of Nb2Pd1-xRuxS5 polycrystalline samples by a solid-state reaction method and systematically investigated the Ru-doping effect on superconductivity by transport and magnetic measurements. It is found that superconductivity is enhanced with Ru doping and is quite robust upon disorder. Hall coefficient measurements indicate that the charge transport is dominated by hole-type charge carriers similar to the case of Ir doping, suggesting multi-band superconductivity. Upon Ru or Ir doping, Hc2/Tc exhibits a significant enhancement, exceeding the Pauli paramagnetic limit value by a factor of approximately 4. A comparison of Tc and the upper critical field （Hc2） amongst the different doping elements on Pd site, reveals a significant role of spin-orbit coupling.