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World Journal of Condensed Matter Physics 2024年第3期14卷 45-50页

作者： gulshan prakash malik Gurugram India Theory Group School of Environmental Sciences Jawaharlal Nehru University New Delhi India

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.

关键词： H3S Upper Critical Field (Hc2) Variation of Hc2 with Temperature Clausius-Clapeyron equation in a magnetic field Behavior of Hc2 for Temperatures Close to 0 K

On the Role of Chemical Potential in Determining the Temperature Dependent Critical Magnetic Field and the Penetration Depth of Superconductors

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World Journal of Condensed Matter Physics 2024年第4期14卷 96-106页

作者： gulshan prakash malik Vijaya Shankar Varma Gurugram India Theory Group School of Environmental Sciences Jawaharlal Nehru University New Delhi India Department of Physics and Astrophysics University of Delhi Delhi India

Dealing with both elemental and high-Tc superconductors (SCs) - Sn, Nb and Pb belonging to the former category, and MgB2 and different samples of YBCO to the latter - we show that the difference in the values of their critical magnetic field Hc1,c2 and the penetration depth λL(0) is, remarkably, attributable predominantly to the difference in the values of a single parameter, viz., the chemical potential (μ) close to their critical temperatures (Tcs). Based directly on the dynamics of pairing in a magnetic field and the corresponding number equation, our approach relates Hc1,c2 of an SC with the following set of its properties: S1 = {μ, Tc, Debye temperature, effective mass of the electron, magnetic interaction parameter, Landau index}. Hence, it provides an alternative to the approach followed by Talantsev [Mod. Phys. Lett. B 33, 1950195 (2019)] who has shown by ingeniously combining the results of various well-established theories that Hc2 of an SC can be calculated via four different equations, each of which invokes two or more properties from its sample-specific set S2 = {Tc, gap, coherence length, λL(0), jump in sp. ht.}, which is radically different from S1.

关键词： Pairing and Number Equations Incorporating Temperature Chemical Potential and Magnetic Field Critical Magnetic Field Penetration Depth Sn Nb Pb MgB2 YBCO

An Inquiry into Two Intriguing Values of the Critical Current Density of Bi-2212

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World Journal of Condensed Matter Physics 2021年第3期11卷 53-64页

作者： gulshan prakash malik Vijaya Shankar Varma B-208 Sushant Lok 1 Gurugram India 180 Mall Apartments Delhi India

The empirically reported values of the critical current density (jc) of Bi-2212 as 2.4 × 105 (jc1;Sample 1) and 1.0 × 106 A/cm2 (jc2;Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 104 G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to jc—a feature to which no heed was paid earlier. The essence of our findings is that the jcs of the two samples differ because they are characterized by different values of the primary variables μi and , where is the effective mass of a charge-carrier and me is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ

关键词： Chemical Potential- Temperature- and Applied Magnetic Field-Dependent Critical Current Density of Superconductors Number Density Landau Quantization Law of Equipartition of Energy Bi-2212

Some Implications of an Alternate Equation for the BCS Energy Gap

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Journal of Modern Physics 2013年第4期4卷 6-12页

作者： gulshan prakash malik Manuel de Llano Instituto de Investigaciones en Materiales Universidad Nacional Autónoma de México Apdo México City México Theory Group School of Environmental Sciences Jawaharlal Nehru University New Delhi India

A set of generalized-BCS equations (GBCSEs) was recently derived from a temperature-dependent Bethe-Salpeter equation and shown to deal satisfactorily with the experimental data comprising the Tcs and the multiple gaps of a variety of high-temperature superconductors (SCs). These equations are formulated in terms of the binding energies W1(T),W2(T),… of Cooper pairs (CPs) bound via one- and more than one-phonon exchange mechanisms;they contain no direct reference to the gap/s of an SC. Applications of these equations so far were based on the observation that for elemental SCs |W01|=△0 at T = 0 inthe limit of the dimensionless BCS interaction parameter λ→0. Here △0 is the zero-temperature gap whence it follows that the binding energy of a CP bound via one-phonon exchanges at T = 0 is 2|W01|. In this note we carry out a detailed comparison between the GBCSE-based W1(T) and the BCS-based energy gap △(T) for all 0≤T≤Tc and realistic, non-vanishingly-small values of λ. Our study is based on the experimental values of Tc Debye temperature , and ?0 of several selected elements including the “bad actors” such as Pb and Hg. It is thus established that the equation for W1(T) provides a viable alternative to the BCS equation for △(T). This suggests the use of, when required, the equation for W2(T) which refers to CPs bound via two-phonon exchanges, for the larger of the two T-dependent gaps of a non-elemental SC. These considerations naturally lead one to the concept of T-dependent interaction parameters in the theory of superconductivity. It is pointed out that such a concept is needed both in the well-known approach of Suhl et al. to multi-gap superconductivity and the approach provided by the GBCSEs. Attention is drawn to diverse fields where T-dependent Hamiltonians have been fruitfully employed in the past.

关键词： BCS and Generalized-BCS Equations T-Dependent Equations for BCS Gap and for Binding Energy of Cooper Pairs Elemental and Composite Superconductors

Compressed H₃S: Fits to the Empirical H_c2(T) Data and a Discussion of the Meissner Effect

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World Journal of Condensed Matter Physics 2023年第4期13卷 111-127页

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.

关键词： Compressed H3S Upper and Lower Critical Fields Chemical Potential Generalized Pairing and Number Equations Coherence Length Penetration Depth Meissner Effect

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

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World Journal of Condensed Matter Physics 2020年第2期10卷 53-70页

作者： gulshan prakash malik Vijaya Shankar Varma B-208 Sushant Lok 1 Gurgaon Haryana India 180 Mall Apartments Delhi India

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.

关键词： Generalized BCS Equations Fermi Energy Critical Current Density Non-Zero Temperatures and Applied Fields Bi-2212

Fermi Energy-Incorporated Generalized BCS Equations for the Temperature-Dependent Critical Current Density and the Related Parameters of a Superconductor for All <i>T</i>≤ <i>Tc</i>and Their Application to Aluminium Strips

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World Journal of Condensed Matter Physics 2019年第3期9卷 47-61页

作者： gulshan prakash malik Vijaya Shankar Varma B-208 Sushant Lok 1 GurgaonHaryanaIndia 180 Mall Apartments Mall RoadDelhiIndia

Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ0, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (VF), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of VF(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.

关键词： jc(T) Data for Superconducting Aluminium Strips Bardeen’s Equation and Kupriyanov-Lukichev Theory for jc(T) Unified Generalized BCS Equations for {Δ Tc jc(T)} T-Dependence of the Sommerfeld Coefficient and Several Other Superconducting Parameters