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The concept of generalized momentum operator which is motivated from the generalized uncertainty principle has been extensively investigated in quantum mechanics and various aspects of theoretical and applied physics. In this study, we have applied this formalism to Ginzburg-Landau theory of superconductvity and Abrikosov vortex lattice in type II-superconductors. After deriving the extended Ginzburg-Landau equations, we have discussed several independent structures of the auxiliary function of position operator in the generalized momentum operator and we have analyzed their features in both Ginzburg-Landau and London theories. Comparable properties to the basic formalism have been obtained even without the presence of the cubic nonlinear term in Ginzburg-Landau equations. However, not all structures of the auxiliary function of position operator result on the exclusion of the magnetic field from a superconductor when it's below its critical temperature. But, only specific forms may succeed to eliminate the magnetic field. This approach has been generalized by considered a position-dependent mass of the electric charge. Amazingly, for a position-dependent mass of hyperbolic soliton-like structure, the extended Ginzburg-Landau wave function is identical to the result obtained in the conventional formalism and besides, for specific correlations between the auxiliary function of the position operator and position-dependent mass, the exclusion of the magnetic field is conceivable. We have also discussed the Abrikosov vortex lattice solution based on the extended Ginzburg-Landau formalism with position-dependent mass of the electric charge. It was observed that, for a specific structure of the position-dependent mass and for a quantum number n = 0 , a transition between a type-II and type-I superconductor takes place if the Ginzburg-Landau parameter is κ = 1 2 1 + 257 ≈ 2.0634. For large n , the problem depends on the asymptotic form of the Hermite polynomial and periodicity occurs if the electric charge is quantized. Further details are obtained and analyzed. [ABSTRACT FROM AUTHOR]

We propose a simplified 2D effective scalar electrodynamics model of relativistic type-II superconductivity. Within this framework, we discuss possible electromagnetic (EM) behaviors of superconductivity along the lines of the nonrelativistic Ginzburg–Landau (GL) theory. This model may be of significance to study very diverse physical phenomena such as a nonlinear version of the electron–hole conversion by a superconductor and electron-positron dynamics around neutron stars. We briefly comment on extending the model to study the 3D dynamics of vortex–vortex interactions and Abrikosov fluxonics. [ABSTRACT FROM AUTHOR]

The iron-based superconductors (IBSs) of the recently discovered 1144 class, unlike many other IBSs, display superconductivity in their stoichiometric form and are intrinsically hole doped. The effects of chemical substitutions with electron donors are thus particularly interesting to investigate. Here, we study the effect of Co substitution in the Fe site of CaKFe 4 As 4 single crystals on the critical temperature, on the energy gaps, and on the superfluid density by using transport, point-contact Andreev-reflection spectroscopy (PCARS), and London penetration depth measurements. The pristine compound ( T c ≃ 36 K) shows two isotropic gaps whose amplitudes ( Δ 1 = 1.4–3.9 meV and Δ 2 = 5.2–8.5 meV) are perfectly compatible with those reported in the literature. Upon Co doping (up to ≈7% Co), T c decreases down to ≃20 K, the spin-vortex-crystal order appears, and the low-temperature superfluid density is gradually suppressed. PCARS and London penetration depth measurements perfectly agree in demonstrating that the nodeless multigap structure is robust upon Co doping, while the gap amplitudes decrease as a function of T c in a linear way with almost constant values of the gap ratios 2 Δ i / k B T c . [ABSTRACT FROM AUTHOR]

Vortices in superconductors can help identify emergent phenomena but certain fundamental aspects of vortices, such as their entropy, remain poorly understood. Here, we study the vortex entropy in underdoped Bi2Sr2CaCu2O8+x by measuring both magneto-resistivity and Nernst effect on ultrathin flakes (≤2 unit-cell). We extract the London penetration depth from the magneto-transport measurements on samples with different doping levels. It reveals that the superfluid phase stiffness ρs scales linearly with the superconducting transition temperature Tc, down to the extremely underdoped case. On the same batch of ultrathin flakes, we measure the Nernst effect via on-chip thermometry. Together, we obtain the vortex entropy and find that it decays exponentially with Tc or ρs. We further analyze the Nernst signal above Tc in the framework of Gaussian superconducting fluctuations. The combination of electrical and thermoelectric measurements in the two-dimensional limit provides fresh insight into high temperature superconductivity. The authors study the vortex entropy in ultrathin flakes of the underdoped cuprate superconductor Bi2Sr2CaCu2O8+x by measuring both magneto-resistivity and Nernst effect. They find that, while the superfluid phase stiffness varies linearly with Tc, the vortex entropy decreases exponentially at lower Tc. [ABSTRACT FROM AUTHOR]

Muon spins precess in transversemagnetic fields and emit a positron preferentially in the spin direction at the instant of decay, enabling muon spin rotation (µSR) as a precise probe of localmagnetic fields in matter. µSR has been used to characterize superconducting radio-frequency (SRF)materials since 2010. At TRIUMF, a beamof 4.2MeV μ+ is implanted at a material-dependent depth of approximately 150 μm. A dedicated spectrometer was developed to measure the field of first vortex penetration and pinning strength in SRF materials in parallel magnetic fields of up to 300mT. A low-energy beam available at PSI implants μ+ at variable depth in the London layer allowing for direct measurements of the London penetration depth from which other material parameters relevant for SRF applications, such as the lower critical field and the superheating field, can be calculated. Beta-detected nuclear magnetic resonance (β-NMR) is a technique similar to low-energy µSR using beams of low-energy β radioactive ions. With a recent upgrade, it is capable of detecting the penetration of parallel magnetic vortices, depth resolved with nanometer resolution at applied fields of up to 200mT. In this paper, we reviewthe impact and capabilities of these techniques for SRF research. [ABSTRACT FROM AUTHOR]

In several theoretical works, it was argued that under certain conditions Abrikosov vortices in multiband superconductors can split and exist in the form of fractional vortices, formed separately in superfluid condensates of different electron bands. Such vortices possess a fractional flux quantum, and these fractional vortices attract each other, trying to join into a composite vortex with the whole flux quantum ϕ 0 = h / 2 e. In the present work, we solve numerically the nonlinear dynamic equation for the composite vortex, settled in the pinning potential well of the columnar defect within a two-band superconductor, and exerted the rf Lorentz force action. We demonstrate that at high enough rf current amplitudes such composite Abrikosov vortices will dissociate into fractional ones and escape from the pinning potential well. The sequence of these events depends on the character of the pinning potential well, e.g., the radius of the pinning potential well. The possible manifestation of such kind transitions in rf electrodynamic characteristics, such as a complex rf resistivity and harmonics generation is calculated. [ABSTRACT FROM AUTHOR]

The effect of the demagnetizing factor, regarding the determination of the de-pairing current density J d e p , has been studied in the case of a Fe(Se,Te) crystal, using DC magnetic measurements as a function of a magnetic field (H) at different temperatures (T). First, the lower critical field H c 1 (T) values were obtained, and the demagnetization effects acting on them were investigated after calculating the demagnetizing factor. The temperature behaviors of both the original H c 1 values and the ones obtained after considering the demagnetization effects ( H c 1 d e m a g ) were analyzed, and the temperature dependence of the London penetration depth λ L (T) was obtained in both cases. In particular, the λ L (T) curves were fitted with a power law dependence, indicating the presence of low-energy quasiparticle excitations. Furthermore, by plotting λ L − 2 as a function of T, we found that our sample behaves as a multigap superconductor, which is similar to other Fe-11 family iron-based compounds. After that, the coherence length ξ values were extracted, starting with the H c 2 (T) curve. The knowledge of λ L and ξ allowed us to determine the J d e p values and to observe how they are influenced by the demagnetizing factor. [ABSTRACT FROM AUTHOR]

The pinning force density, F p , is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum, F p , m a x , which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of F p , m a x on the average grain size, d , in Nb3Sn-based conductors. F p , m a x d datasets were analyzed and a scaling law for the dependence F p , m a x d = A × l n 1 / d + B was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at T = 4.2   K and d ≥ 650   nm , Nb3Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available F p , m a x d data for Nb3Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, δ , varies within a remarkably narrow range of δ = 175 ± 13   nm for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near grain boundary surfaces (similar to London's law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ , and the surface is a superconductor–vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries. [ABSTRACT FROM AUTHOR]

Following the discovery of superconductivity by Heike Kamerlingh Onnes in 1911, research concentrated on the electric conductivity of the materials investigated. Then, it was Max von Laue who in the early 1930s turned his attention to the magnetic properties of superconductors, such as their demagnetizing effects in a weak magnetic field. As a consultant at the Physikalisch-Technische Reichsanstalt in Berlin, von Laue was in close contact with Walther Meissner at the Reichsanstalt. In 1933, Meisner together with Robert Ochsenfeld discovered the perfect diamagnetism of superconductors (Meissner–Ochsenfeld effect). This was a turning point, indicating that superconductivity represents a thermodynamic equilibrium state and leading to the London theory and the Ginzburg–Landau theory. In the early 1950s in Moscow, Nikolay Zavaritzkii carried out experiments on superconducting thin films. In the theoretical analysis of his experiments, he collaborated with Alexei A. Abrikosov and for the first time they considered the possibility that the coherence length ξ can be smaller than the magnetic penetration depth λ m . They called these materials the "second group". Subsequently, Abrikosov discovered the famous Abrikosov vortex lattice and the superconducting mixed state. The important new field of type-II superconductivity was born. [ABSTRACT FROM AUTHOR]

In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental studies. Superconductivity in hydrides has been primarily explored by electrical transport measurements, whereas magnetic properties, one of the most important characteristic of a superconductor, have not been satisfactory defined. Here, we develop SQUID magnetometry under extreme high-pressure conditions and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m-LaH10—the representative members of two families of high-temperature superconducting hydrides. We determine a lower critical field Hc1 of ∼0.82 T and ∼0.55 T, and a London penetration depth λL of ∼20 nm and ∼30 nm in H3S and LaH10, respectively. The small values of λL indicate a high superfluid density in both hydrides. These compounds have the values of the Ginzburg-Landau parameter κ ∼12–20 and belong to the group of "moderate" type II superconductors, rather than being hard superconductors as would be intuitively expected from their high Tcs. Superconductivity in hydrides has been primarily explored by electrical transport measurements. Here, the authors perform SQUID magnetometry under extreme high-pressure and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m- LaH10—the representative members of two families of high-temperature superconducting hydrides. [ABSTRACT FROM AUTHOR]

The lower critical field, Bc1, is one of the fundamental quantities of a superconductor that directly manifests the Cooper pair bulk density in the material. Although this field can be measured using several techniques, the most conventional method is to calculate this field from the experimentally measured DC penetration field, Bp, which is defined as the starting point of the deviation of the DC magnetization curve, M(Bappl), from a linear dependence. Surprisingly, we found no mathematical routine that describes how this starting point of deviation can be found. Here, we propose the extraction of Bp from the fit of the M(Bappl) dataset to the power law, where the threshold criterion Mc can be established by a convention. The advantage of this approach is that the procedure extracts one additional characteristic parameter: the power-law exponent. We demonstrated the applicability of this approach to polycrystalline ThIr3, WB4.2, BaTi2Bi2O, and Th4H15; thin films of Pb and MgB2; and Nb single crystal. In most reports, Bc1(T) analysis is limited by the extraction of the London penetration depth. We advanced the analysis to extract primary thermodynamic superconducting parameters [i.e., the ground state superconducting energy gap, Δ(0); the relative jump in electronic specific heat at transition temperature, Δ C γ T c ; and the gap-to-transition temperature ratio, 2 Δ 0 k B T c ] from Bc1(T) data. This extraction was performed for Nb, ThIr3, TaRh2B2, and NbRh2B2. [ABSTRACT FROM AUTHOR]

Superconductivity is analysed based on the productlike fractal measure approach with fractal dimension a introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on the position of the electrons. Several physical quantities were found to be position-dependent comparable with those arising in heavy doping and p-n junction. At the boundary of the superconductor, a shrinkage of the magnetic field was observed, leading to a scenario equivalent to the Meissner-Ochsenfeld effect. An enhancement of the London penetration depth is revealed and such an improvement was observed in pnictides at the onset of commensurate spin-density-wave order inside the superconducting phase at zero temperature. The Bardeen-Cooper-Schrieffer theory was also analysed and the appearance of zero-energy states is detected. Nucleation of superconductivity in a bulk was also studied. The system acts as a quantum damped harmonic oscillator and our analysis showed that type-I superconductivity occurs when k < √2/(1 + α), whereas type II occurs for k > √2/(1 + α), where k is the Ginzburg-Landau parameter. The transition at the passage from the 'genuine' to the 'intermediate' type-I estimates 0.767767 <α ≤ 1. [ABSTRACT FROM AUTHOR]

A dissipation-free current is one of the most fascinating and practically important properties of superconductors. At self-field conditions (when no external magnetic field is applied) dissipation-free current density, Jc(sf, T), in thin weak-link-free superconductors described by the equation (where λ(T) is the London penetration depth, and κ is the Ginzburg–Landau parameter) was proved for more than 90 superconductors, including type-I and type-II superconductors, elementary superconductors, pnictides, cuprates, MgB2, heavy fermions and H3S. In addition, it was recently proposed for quasi-two dimensional superconductors (namely pnictides and cuprates), that maximum achievable critical current density, Jc(sf, T ∼ 0 K), is linked with the transition temperature, Tc, and the mean spacing between superconducting sheets, d, by the following equation: (Talantsev and Crump 2018 Supercond. Sci. Technol.31 124001). In this paper, we focused on the inverse problem, i.e., to find the best candidates for the developing practical wires in terms of their self-field critical current capacity from known parameters of newly discovered superconductors (for which we draw largely on Hosono et al 2015 Sci. Technol. Adv. Mater.16 033503). Considering that in-field critical currents of iron-based superconductors are very slow functions of applied magnetic fields, our calculations may have wider applicability outside self-field conditions. [ABSTRACT FROM AUTHOR]

We numerically studied vortex configurations in superconducting isosceles right triangles. We found the solution of the London equation using Green’s function method. Then the Gibbs free energy for an arbitrary configuration was obtained. Using molecular dynamic simulation, we calculated the stable configurations for specific vorticities. The filling rulers were revealed by analyzing these states. Moreover, by changing the sample size, we found that many configurations are sensitive to sample size, which shows a very strong size effect. Lastly, general rules of the size effect were summarized. [ABSTRACT FROM AUTHOR]