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A simplified model of anisotropic magnetic susceptibility in the Meissner–London vortex-free state of cuboidal superconducting samples is presented. Using this model, precision measurements of the magnetic response in three perpendicular directions of a magnetic field with respect to primary crystal axes can be used to extract the components of the London penetration depth, thus enabling the evaluation of the general superfluid density tensor, which is needed in the analysis of the superconducting gap structure. [ABSTRACT FROM AUTHOR]

We provide a thermodynamic derivation of the only-phase Popov action functional, which is often adopted to study the low-energy effective hydrodynamics of a generic nonrelativistic superfluid. It is shown that the crucial assumption is the use of the saddle point approximation after neglecting the quantum-pressure term. As an application, we analyze charged superfluids (superconductors) coupled to the electromagnetic field at zero temperature. Our only-phase and minimally-coupled theory predicts the decay of the electrostatic field inside a superconductor with a characteristic length much smaller than the London penetration depth of the static magnetic field. This result is confirmed also by a relativistic only-phase Popov action we obtain from the Klein–Gordon Lagrangian. [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]

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]

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]

We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D'Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu–Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency. [ABSTRACT FROM AUTHOR]

In this article, we investigated the structural, electronic, mechanical, optical, and superconducting state properties of the trichalcogenides, MTe3(M = Hf, Zr) compounds using the density functional theory. Electronic energy dispersion curves demonstrate that the title compounds are metallic in nature, with a significant contribution from the Te atom. The technologically important mechanical properties (stiffness constant, elastic moduli, brittle/ductile behavior, Poisson's ratio, elastic anisotropy, machinability index, and hardness) are thoroughly examined and addressed. The value of Pugh's ratio indicates the ductility (brittleness) of ZrTe3 (HfTe3). The Vickers hardness value is 0.86 and 0.54 GPa for MTe3 (M = Hf, Zr), respectively, which confirms their softness. The value of lattice thermal conductivity (in W m−1 K−1) for HfTe3 (3.64) and ZrTe3 (2.36) is low due to significant phonon scattering as confirmed by the Grüneisen parameter study. The optical constants were computed, which confirmed the strong optical anisotropy of MTe3 (M = Hf, Zr). For ZrTe3, with the electric field polarization along the [100] direction, the highest reflectivity (51.36%) is obtained compared to HfTe3 (45.21%). This shows promise for application as a radiative heat reflector of these two compounds. The superconducting state properties, such as London penetration depth, coherence length, Ginzburg–Landau parameter, and electron–phonon coupling parameters are estimated and discussed. The value of electron–phonon coupling parameters suggests that both compounds are moderately coupled superconductors. [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]

For practical applications of superconductors, understanding the vortex matter and dynamics is of paramount importance. An important issue in this context is the transition of the vortex glass, which is a true superconducting phase, into a vortex liquid phase having a linear dissipation. By using multi-harmonic susceptibility studies, we have investigated the vortex glass—vortex liquid phase transitions in CaKFe4As4 and BaFe2(As0.68P0.32)2 single crystals. The principle of our method relates the on-set of the third-harmonic susceptibility response with the appearance of a vortex-glass phase in which the dissipation is non-linear. Similar to the high-critical temperature cuprate superconductors, we have shown that even in these iron-based superconductors with significant lower critical temperatures, such phase transition can be treated as a melting in the sense of Lindemann's approach, considering an anisotropic Ginzburg-Landau model. The experimental data are consistent with a temperature-dependent London penetration depth given by a 3D XY fluctuations model. The fitting parameters allowed us to extrapolate the vortex melting lines down to the temperature of liquid hydrogen, and such extrapolation showed that CaKFe4As4 is a very promising superconducting material for high field applications in liquid hydrogen, with a melting field at 20 K of the order of 100 T. [ABSTRACT FROM AUTHOR]

For the conventional superconductors it will be shown that not only the superconducting energy gap, Egap(T=0), and the critical field, Bc(T=0), but also the London penetration depth, λL(T=0), scale in a reasonable approximation with the superconducting transition temperature, TSC, as ~TSC, ~TSC 2 and ~T-1/2, respectively. From these scaling relations the conclusion obtained earlier, using a completely different method, is confirmed that the London penetration depth corresponds to the diameter of the Cooper-pairs. As a consequence, only one layer of Cooper pairs is sufficient to shield an external magnetic field completely. The large diamagnetism of the superconductors is caused by the large orbital area of the Cooper-pairs. From the fact that, in the zero-field ground state, the temperature dependence of the superconducting heat capacity is given above and below TSC by power functions of absolute temperature it follows that the only critical point is T=0. The superconducting transitions of the element superconductors, therefore, are all within the critical range at T=0. As a consequence, above and below TSC there is short-range order only. As we know from Renormalization Group (RG) theory, in the critical range the dynamics is the dynamics of a boson field, exclusively. Evidently, the Cooper-pairs have to be considered as the short-range ordered units created by this boson field. It is reasonable to assume that the relevant bosons in the superconducting state are identical with the bosons giving rise to the universal linear-in-T electronic heat capacity above TSC. Plausibility arguments will be given that these bosons must be electric quadrupole radiation generated by the non-spherical charge distributions in the soft zones between the metal atoms. The radiation field emitted by an electric quadrupole can be assumed to be essentially curled or circular. In the ordered state below TSC, the bosons are condensed in resonating spherical modes which encapsulate the two Cooper-pair electrons and shield their charge perfectly. [ABSTRACT FROM AUTHOR]

Guided by Pippard superconductivity, we incorporate the Seiberg–Witten map in the classical London theory of Type-I superconductors when an external magnetic field is applied. After defining the noncommutative Maxwell potentials, we derive the London equation for the supercurrent as a function of the noncommutative parameter, up to second order in gauge fields expansions. Keeping track of the effects of noncommutative gauge fields, we argue that noncommutative magnetic field effects can be cast in the London penetration length similar to nonlocal Pippard superconductivity. Also, we show that the flux quantization remains consistent relative to the commutative case. Our effective London penetration length reduces to the standard one in the commutative limit. These results allow us to argue that the framework of noncommutative electrodynamics can give some insights into the anisotropic and nonlocal structure of superconductivity and Condensed Matter Systems, perhaps out of the ultra-microscopic scale regime. [ABSTRACT FROM AUTHOR]

The properties of a hybrid structure with the proximity effect, which consists of a ferromagnetic insulator (FI) disk resting on the surface of a thin s-type superconductor film, at the boundary of which the Rashba spin–orbit (SO) interaction plays a significant role, are investigated in the London approximation. The joint action of the spin splitting and the SO interaction leads to the generation of a spontaneous supercurrent and induces Pearl vortices located on the perimeter of the disk in the film. The supercurrent distribution in the field and the structure of the magnetic field induced by it are calculated for FI disks with a radius of about the effective field penetration depth Λ in the superconductor, for which the screening effects become significant. The structure of the vortex state consisting of several vortex–antivortex pairs is analyzed, and the condition of switching between different vortex configurations are determined. The possibility of full compensation of the spontaneous supercurrent produced by the SO interaction and the exchange field by circulating current of a dense chain of vortices at the disk boundary is demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents the effects of non-minimal Lorentz-violation operators in superconductivity. By constructing a Lorentz-Violating Ginzburg–Landau theory of superconductivity with a five-dimensional operator, we discuss the influence of higher dimensional Lorentz-Violating operators in the London's depth penetration, in the coherence length and critical magnetic field. • The influence of a higher dimensional Lorentz-Violating operator in the London's depth penetration, in the coherence length and critical magnetic field that breaks the superconducting state. • The critical magnetic field is insensitive to the Lorentz-violating contributions. • The critical magnetic field for type II superconductors is affected by the Lorentz-violating contributions. • The London's depth penetration is drastically modified by the presence of the Lorentz-violating contributions. • Under certain conditions controlled by the Lorentz-violating contribution, there exists a first-order phase transition between the superconducting state and an insulating state. [ABSTRACT FROM AUTHOR]

The London penetration depth λ is the basic length scale for electromagnetic behavior in a superconductor. Precise measurements of λ as a function of temperature, field and impurity scattering have been instrumental in revealing the nature of the order parameter and pairing interactions in a variety of superconductors discovered over the past decades. Here we recount our development of the tunnel-diode resonator technique to measure λ as function of temperature and field in small single crystal samples. We discuss the principles and applications of this technique to study unconventional superconductivity in the copper oxides and other materials such as iron-based superconductors. The technique has now been employed by several groups world-wide as a precision measurement tool for the exploration of new superconductors. [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]

Superconductors are popular for microwave engineers because they are high performance, high selectivity, and low volume. However, the use of superconductors is limited due to their inherent nonlinearity. Intrinsic nonlinearity in superconductors is due to the dependence of surface current density on the depth of London penetration in them. This leads to adverse effects such as intermodulation distortion (IMD) and the production of a third harmonic in a superconductor. In this article, we intend to improve the effects of nonlinearity by modifying the superconducting geometric structure, which we call the method of geometric reconstruction. To achieve this, we first designed a superconducting transmission line (TL), and then created slots on the superconducting TL to improve the IMD and the third harmonic. Using this method, we managed to reduce the level of the third harmonic from –6 to –31 dBm. To verify the results, after simulating the slotted superconducting TL in ADS software, simulation and solving of London equations using three-dimensional-FEM in COMSOL software has been done again. [ABSTRACT FROM AUTHOR]

The entry of fractional vortices and their subsequent dynamics inside a two-band superconductor is explored based on the numerical solutions of time-dependent Ginzburg–Landau (TDGL) equations. We consider the case when superfluid electron condensates from two zones are characterized by quite different parameters, such as coherence lengths ξi, and London penetration depths λi, which in turn leads to the different critical magnetic fields Hc,iand fractional flux quanta ϕivalues for the superconducting state in these two zones. Numerical solutions of TDGL equations in increasing external magnetic field followed by mathematical modeling of magnetic flux penetration were performed for this case by finite element method. We have explored the time evolution for the fractional vortices penetration process and their subsequent dynamics inside the specimens for two geometries: the circular disk, and the circular disk with a triangular cutout. Obtained results indicate that magnetic flux penetrates inside the specimen in the form of fractional vortices when they can overcome the edge barrier, which may be different for these two vortex types. Therefore, in increasing external magnetic field first penetrate vortices with a lower barrier height (i.e., lower Hc,i) while the other type of fractional vortices start their penetration at higher external field value. Another mechanism for the formation of fractional vortices during their entrance in a two-band superconductor is related to the difference in their flux values and viscosity coefficients which determine the rate of vortex proliferation inside the sample. Within the specimen, fractional vortices move in order to arrange. Vortices of different types attract to each other and try to stick together thus forming composite vortices with the whole flux quantum value ϕ0 = h/2e. [ABSTRACT FROM AUTHOR]

One of the features of the unconventional state in iron-based superconductors is possibility to transform to the s++ state with the increase of the nonmagnetic disorder. Detection of such a transition would prove the existence of the state. Here we study the temperature dependence of the London magnetic penetration depth within the two-band model for the and s++ superconductors. By solving Eliashberg equations accounting for the spin-fluctuation mediated pairing and nonmagnetic impurities in the T-matrix approximation, we have derived a set of specific signatures of the transition: (1) sharp change in the behavior of the penetration depth λL as a function of the impurity scattering rate at low temperatures; (2) before the transition, the slope of increases as a function of temperature, and after the transition this value decreases; (3) the sharp jump in the inverse square of the penetration depth as a function of the impurity scattering rate, , at the transition; (4) change from the single-gap behavior in the vicinity of the transition to the two-gap behavior upon increase of the impurity scattering rate in the superfluid density ρs(T). [ABSTRACT FROM AUTHOR]

Available data of the temperature dependence of the superconducting heat capacity and of the thermal conductivity of the conventional superconductors are analyzed in detail. It is shown that in contrast to the exponential function predicted by the BCS theory, the temperature dependence of the superconducting heat capacity consists of a sequence of a few analytically different universal power functions of absolute temperature. The changes from one to the next power function are typical examples of crossover events. The crossover occurring at the lowest temperature, commonly below about ~1 K, is identified as transition from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as the mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. Since TBE is proportional to ~n2/3, with n as the density of the Cooper pairs at TBE, it is possible to obtain the density of the Cooper pairs at low temperatures. Assuming that for the type I superconductors the Cooper pairs form a dense gas of bosons with virtually no space between them, the diameter of the Cooper-pair orbital, calculated from n2/3, turns out to agree quantitatively with the experimental value of the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely. [ABSTRACT FROM AUTHOR]

Identifying the uniqueness of FeP-based superconductors may shed new lights on the mechanism of superconductivity in iron-pnictides. Here, we report nuclear magnetic resonance (NMR) studies on LiFeP and LiFeAs which have the same crystal structure but different pnictogen atoms. The NMR spectrum is sensitive to inhomogeneous magnetic fields in the vortex state and can provide the information on the superconducting pairing symmetry through the temperature dependence of London penetration depth λL. We find that λL saturates below T ∼ 0.2 Tc in LiFeAs, where Tc is the superconducting transition temperature, indicating nodeless superconducting gaps. Furthermore, by using a two-gaps model, we simulate the temperature dependence of λL and obtain the superconducting gaps of LiFeAs, as Δ1 = 1.2 kBTc and Δ2 = 2.8 kBTc, in agreement with previous result from spin-lattice relaxation. For LiFeP, in contrast, λL does not show any saturation down to T ∼ 0.03 Tc, indicating nodes in the superconducting gap function. Finally, we demonstrate that strong spin fluctuations with diffusive characteristics exist in LiFeP, as in some cuprate high temperature superconductors. [ABSTRACT FROM AUTHOR]

Identifying the form of superconducting order parameter is still a controversial problem for the iron-based superconductor FeSe. Based on anisotropic two-component Ginzburg–Landau theory, we study the temperature dependence of upper critical field and London penetration depth for FeSe. Without including the spin paramagnetic effect, all of our theoretical calculations fit the experimental data well in a broad temperature range. Our results thus show that FeSe is a two-gap s-wave superconductor. And the anisotropy of effective masses in the band with larger (or smaller) gap can be estimated as about 10 (or 2) respectively. [ABSTRACT FROM AUTHOR]

Using magnetic force microscopy operating at sub-Kelvin temperatures, we characterize the heavy fermion superconductor CeCoIn5. We pinpoint the absolute London penetration depth of λ (0) = 435 ± 20 nm and report its temperature dependence, which is closely linked to the symmetry of the superconducting gap. In addition, we directly measure the pinning force of individual Abrikosov vortices and estimate the critical current density of j c = 9 × 10 4 A/cm2. In contrast to the related, well-established tunnel diode oscillator technique, our method is capable of resolving inhomogeneities locally on the micrometer scale at ultra-low temperature. [ABSTRACT FROM AUTHOR]

We demonstrate a geometrical effect on the depinning line (DL) of the flux line lattice of the Bi2Sr2CaCu2O8+δ high-Tc superconductor (HTSC) micrometer ring. The DL shifts to notably lower temperatures in comparison with bulk crystals and thin flakes of the same sample. The shift is attributed to a decrease in the overall pinning potential due to a double size effect, namely (a) the ring thickness ∼ 1 μ m being smaller than the pinning correlation length and (b) the increase in the effective London penetration depth of the vortices (Pearl vortices). The large shift of the DL to lower temperatures may influence the suitability of this HTSC for applications in microstrip antennas and THz emitters. [ABSTRACT FROM AUTHOR]

This work reports superconductivity studies in the intermetallic Ti0.85Pd0.15 performed in normal conditions and under hydrostatic pressure. The crystal structure of the compound has a body-centered cubic at room temperature and atmospheric pressure as unstable β-Ti phase. X-ray diffraction pattern shows space group I m 3 ̄ m with parameter a = 3.2226(4) Å and density around 5.6242 g/cm3. The superconducting transition temperature, TC = 3.7 K was determined from resistance, magnetization, and specific heat measurements. The two critical magnetic fields, the coherence length, Ginzburg–Landau parameter, London penetration depth, the superconducting energy gap, the Debye temperature, the electron-phonon coupling constant and density of states at the Fermi level were calculated. These parameters were obtained at ambient pressure. Under hydrostatic pressure, the magnetic susceptibility measurements show a small increment on TC, the maximum TC = 3.83 K was obtained at the maximum applied pressure of 1.03 GPa. The slope calculated for TC as a linear function of pressure was about 0.14 K/GPa, possibly associated with an increase in the electronic density of states. [ABSTRACT FROM AUTHOR]

A type I superconductor expels a magnetic field from its interior to a surface layer of thickness λ L , the London penetration depth. λ L is a function of temperature, becoming smaller as the temperature decreases. Here we analyze the process of cooling (or heating) a type I superconductor in a magnetic field, with the system remaining always in the superconducting state. The conventional theory predicts that Joule heat is generated in this process, the amount of which depends on the rate at which the temperature changes. Assuming the final state of the superconductor is independent of history, as the conventional theory assumes, we show that this process violates the first and second laws of thermodynamics. We conclude that the conventional theory of superconductivity is internally inconsistent. Instead, we suggest that the alternative theory of hole superconductivity may be able to resolve this problem. [ABSTRACT FROM AUTHOR]

In this study, we present the recent insights into the origin of the high-field Q-slope in superconducting radio frequency cavities. Consequent hydrofluoric acid rinses are used to probe the radio frequency performance as a function of the material removal of two superconducting bulk niobium cavities prepared with low temperature nitrogen infusion. The study reveals that nitrogen infusion affects only the first few tens of nanometers below the native oxide layer. The typical high-field Q-slope behavior of electropolished cavities is indeed completely recovered after a dozen hydrofluoric acid rinses. The reappearance of the high-field Q-slope as a function of material removal was modeled by means of London's local description of screening currents in the superconductor, returning good fitting of the experimental data and suggesting that a layer of interstitial impurities with diffusion length on the order of tens of nanometers can mitigate high-field Q-slope. [ABSTRACT FROM AUTHOR]

It is suggested that the difference between the normal and the superconducting state is that the individual electronic states in the proximity of the Fermi level are standing wave states. Superconductivity may then be understood as a condensation of standing wave states. All other properties of superconductors and specifically their electrodynamic behavior are direct consequences of this single property. The London relation may be understood as a microscopic relation of single particles. The understanding gained provides a path for design of new superconductors. [ABSTRACT FROM AUTHOR]

In this article we revisit a well-known effect in superconductors, which is the penetration of the magnetic field by regions of greater radius of curvature (Tinkham, 2008; De Gennes, 1966). This is exposed in the literature but without a quantitative solution. Here we solve this problem by two distinct numerical simulations. We calculate the superconducting current density using numerical simulations via the London theory in the Meissner state and numerical simulations using the time-dependent Ginzburg–Landau (TDGL) theory for the vortex state. In both simulations, the results obtained are in agreement, as could not be otherwise. We show that in the Meissner state the current density increases much faster in the region where the radius of curvature is larger, thus reaching the critical value first in this location, and therefore local breakdown of superconductivity occurs. In the vortex state, our simulations, using TDGL, show that the vortices penetrate through exactly the same location pointed out by the previous simulation. For this study we worked with a superconducting needle with an ellipsoidal mesoscopic cross section. • London theory is used to determine the increase in Js along the superconducting needle in the Meissner state. • TDGL theory is used to study the penetration of vortices into the superconducting needle. • The supercurrent Js is greater at points with a larger radius of curvature. • The penetration of the first vortices occurs through the points with the greatest radius of curvature, that is, where Js is greatest. [ABSTRACT FROM AUTHOR]

Fractional calculus (FC) is a valuable tool in the modeling of many phenomena, and it has become a topic of great interest in science and engineering. This mathematical tool has proved its efficiency in modeling the intermediate anomalous behaviors observed in different physical phenomena. The Meissner–Ochsenfeld effect describes the levitation of superconductors in a nonuniform magnetic field if they are cooled below critical temperature. This paper presents analytical solutions of the fractional London equation that describes the Meissner–Ochsenfeld effect considering the Liouville–Caputo, Caputo–Fabrizio–Caputo, Atangana–Baleanu–Caputo, fractional conformable derivative in Liouville–Caputo sense and Atangana–Koca–Caputo fractional-order derivatives. Numerical simulations were obtained for different values of the fractional-order. [ABSTRACT FROM AUTHOR]

Abstract We characterize thermally quench condensed (~80 K) Sn thin films of two different thicknesses to explore their usefulness for vortex studies. The coherence length and the London penetration depth near the critical temperature indicate that the thin films are in the dirty limit and behave as type II superconductors. Furthermore, when we add ferromagnetic nanostripes on top of the Sn thin films, the ferromagnet-superconductor hybrids show hysteric and anisotropic behavior. A ferromagnet-superconductor hybrid with a thinner Sn film exhibits a stronger effect. Highlights • Thermally quench condensed superconducting Sn thin films in ferromagnet-superconductor hybrids. • The Sn thin films behave as Type II superconductors in the dirty limit. • The ferromagnet-superconductor hybrids with thinner Sn films exhibit stronger interactions. [ABSTRACT FROM AUTHOR]

Using the approach of strong coupling Eliashberg theory the London penetration depth (λL) function of strained Nb2InC compound has been obtained. Studied system belongs to the large family of MAX phases which share good thermal, electrical, and mechanical properties. This is the result of layered structure ensuring both good metallic and ceramic characteristics. Such combination could be of great use as long superconducting ribbons or planes composed with other flexible material. This paper examines the effect of magnetic field penetration inside superconducting material under applied current. Applied biaxial strain with values between -10% and 10% was taken into consideration. Obtained results indicate the possible amendment of the magnetic penetration depth (λL) with the use of strain applied to the material. Highest value of the London penetration depth is reported in case of strains maintaining the highest critical temperature. Reduction of λL(0) value to the least in the region of lowest Tc can be observed. This implies greater protection against supercurrent vortices breaking superconducting state. [ABSTRACT FROM AUTHOR]

The transport critical current, Ic, is usually defined in terms of a threshold electric field criterion, Ec, with the convention Ec = 1 μV/cm chosen somewhat arbitrarily to provide “reasonably small” electric power dissipation in practical devices. Thus Ic is not fundamentally determined. However, recently it has been shown that the self-field critical current of thin-film superconductors is indeed a fundamental property governed only by the London penetration depth of the material. Here we reconsider the definition of the critical current and resolve this apparent contradiction. We measure the field distribution across the width of both first-generation and second-generation high-temperature superconducting tapes as the transport current is increased from zero to Ic.We identify a threshold current, Ic,surfB, at which the local surface magnetic flux density, Bsurf, abruptly crosses over from a non-linear to a linear dependence on the transport current, as measured at any point on the superconductor surface. This results from the current distribution across the tape width transitioning from non-uniform to uniform. This coincides with the onset of dissipation and immediately precedes the appearance of a measureable electric field. In the present examples Ic,surfB is 12–15% lower than an Ic determined by the Ec criterion. We propose the transition of Bsurf(I) from non-linear to linear as a more fundamental criterion for determining transport critical currents. [ABSTRACT FROM AUTHOR]

The layered bismuth oxy-sulfide materials, which are structurally similar to Fe-pnictides/chalcogenides and cuprates superconductors, have sparked a lot of interest in the physics of reduced-dimensional superconductors. The pairing symmetry of the recently discovered BiCh 2 -based superconductor, La 1−x Ce x OBiSSe with x = 0.3, was investigated using zero-field and transverse field (TF) muon spin measurements, as well as using magnetization and resistivity measurements. Resistivity and magnetization data confirmed bulk superconductivity below 2.7 K for x = 0.3. The temperature dependence of the magnetic penetration depth has been determined from TF- μ SR data, which can be described by an isotropic two-gap s + s wave model compared to a single gap s - or anisotropic s -wave model, which resembles with Fe-pnictides/chalcogenides and MgB 2. Furthermore, from the TF- μ SR data, we have determined the London's penetration depth λ L (0) = 452(3) nm, superconducting carrier's density n s = 2.18(1) × 1026 carriers/m3 and effective mass enhancement m ∗ = 1.66(1) m e , respectively. No signature of spontaneous internal field is found down to 100 mK in ZF- μ SR measurement, which suggests that time-reversal symmetry is preserved in this system. • Layered bismuth oxy-sulfide materials, reduced-dimensional superconductors. • Superconducting pairing symmetry using ZF-, TF- μ SR. • Bulk superconductivity below 2.7 K for x = 0. 3. • Multigap s + s wave superconductivity. • Preserved time-reversal symmetry. [ABSTRACT FROM AUTHOR]

We report measurements of London penetration depth λ(T) for the noncentrosymmetric superconductor BiPd by using a tunnel diode oscillator. Pronounced anisotropic behavior is observed in the low-temperature penetration depth; the in-plane penetration depth λac(T) follows an exponential decrease, but the interplane penetration depth λb(T) shows power-law-type behavior. The superfluid density ρs(T), converted from the penetration depth λ(T), is best fitted by an anisotropic two-band BCS model. We argue that such a complex order parameter is attributed to the admixture of spin-singlet and spin-triplet pairing states as a result of antisymmetric spin-orbit coupling in BiPd. [ABSTRACT FROM AUTHOR]

In this note, we analyze the classical magneto-static approach to the theory of type I superconductors, and a Debye source representation that can be used numerically to solve the resultant equations. We also prove that one of the fields, J − , found within the superconductor via the London equations, is the physical current in that the outgoing part of the magnetic field is given as the Biot-Savart integral of J −. Finally, we compute the static currents for moderate values of London penetration depth, λ L , for a sphere, a stellarator-like geometry and a two-holed torus. • Uniqueness result for Maxwell/London equations on non-contractible domains. • A Debye source integral representation for the solution of Maxwell/London equations. • Proof that the static current inside the superconductor is the physical current. • High order accurate solvers for computing static currents in non-contractible domains. [ABSTRACT FROM AUTHOR]

In the present paper, we attempt to bring to light some of the hidden variables of quantum mechanics by continuing the work of others who introduced constant curvature to spacetime. The article is also a continuation of a previous one [S. Koutandos, Phys. Essays 33, 208 (2020)] published in this journal proving London equations. We find that there is dilation of volume and that mass may have a surface density. Unlike the case of superconductors, however these surfaces collapse to a point. This is where the difficulty in measurement comes from. [ABSTRACT FROM AUTHOR]

A photonic crystal (PC) having the structure (AB)NA is investigated. A and B are superconductor and dielectric layers, respectively. P-polarized (TM) wave is assumed to be incident on the PC. The transmission of TM waves through the PC is studied with a focus on photonic band gap (PBG). The change in the PBG is studied with the variation of different parameters of the superconducting layer such as temperature, critical temperature, thickness and London penetration length. The angle of incidence dependence of the PBG is also investigated. The PBG band width at half maximum (BWHM) decreases with increasing the incidence angle until Brewster angle is reached where the band gap vanishes. The BWHM has shown the lowest dependence on temperature and critical temperature among the parameters of the superconducting layer. London penetration length has the greatest effect on the BWHM among the parameters of the superconductor layer. [ABSTRACT FROM AUTHOR]

The defining property of every three-dimensional ε -contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η -Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S 3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory. [ABSTRACT FROM AUTHOR]

• A new RG functional form of the pinning force density in superconductor in the critical state model is suggested. • Numerically internal field profile below critical temperature has been calculated. • Numerical internal field profile exhibits non-London nature of variation. • Grain radius and temperature affect internal field profile. • Numerically ac susceptibility has been calculated. • Peak in the imaginary part of the susceptibility with T is sensitive to the grain radius. The penetration of the magnetic field in a network consisting of the superconducting grains and intergranular region depends not only on the applied external magnetic field but also on the underlying pinning force density and fraction of the superconducting grains in the sample. Considering the underlying pinning force density in the form of the repetitive Gaussian (RG) nature we have solved the critical state model to get the spatial internal field profile at a particular time instant. The internal magnetic field as a function of the position inside the superconductor exhibits nonlinear, step-like nature. The complicated nature of the penetration of the field gets strongly affected by the size of the granular region and the total pinning force density in the superconductors. We have numerically calculated the real and imaginary parts of the complex susceptibility. The variation of the imaginary part with the temperature has a peak at a temperature which shifts towards the higher temperature with the reduction of the superconducting fraction. [ABSTRACT FROM AUTHOR]

• We introduce a new quantization scheme for the charge inside a superconductor. • We obtain the exact quantum solutions for charge space in a superconductor with time-dependent parameters. • We calculated the time-dependent uncertainties and the mean energy of the system. • Information measures, such as Shannon entropy and complexity were calculated. The main goal of this paper is to obtain the exact quantum solutions for charge space in a superconductor with time-dependent parameters using the London approach. We introduce a new quantization scheme for the charge inside a superconductor based on the Lewis and Riesenfeld invariant operator method. From the wave-functions obtained, we calculated the time-dependent uncertainties and the mean energy of the system. Information measures were also obtained, such as Shannon entropy and complexity. The later is always time-independent and also does not depend on conductivity. The other quantities are written in terms of a time-dependent function, ρ (t) , c-number quantity satisfying a nonlinear differential equation. [ABSTRACT FROM AUTHOR]

• Magnetic response of rotating superconductors is discussed. • Critical fields of superconductors can be increased or decreased due to the mechanical rotation. • Vortex physics in rotating superconductors is presented. It is generally believed that, at a certain temperature below the critical one, magnetic response of a superconductor (SC) is determined solely by its intrinsic properties. Here we show that the mechanical rotation of a SC can easily change the values of the critical fields at which the superconductivity is destroyed (type-1 SC) or the vortices penetrate into (exit from) the material (type-2 SC). This is due to a superposition of the Meissner current induced by the external field, and the spontaneous current on the surface of the SC induced by the mechanical rotation. As a result, the critical fields of a SC can be increased or decreased, depending on the geometrical form of the material and the relative orientation of rotation and the external field. [ABSTRACT FROM AUTHOR]

We report on the superconductive paired states in TbPdBi, β-type FeSe and CaSn 3 single crystals through temperature dependence of magnetic penetration depth analysis down to 0.040 K. For half-Heusler TbPdBi, in ultra-low temperature region we traced the T3 power-law behavior of penetration depth indicating the nodeless topological superconductivity with anisotropic gap structure which was confirmed with the analysis of superfluid density. That highlights the role of thermally activated quasi-particles in the pairing mechanism of TBPdBi for which the variation of Δλ(T) wanders off the renown quadratic behavior of penetration depth. In FeSe the contribution of London depth was described with a power law (n ≈ 2.4) and the superfluid density fitted well with two-band d + d model in which the values of both gaps are substantially smaller than the gap size expected by the isotropic BCS model, due to the nodeless anisotropic gap symmetry. In CaSn 3 , temperature variation of magnetic penetration depth exhibited linear behavior which is ascribed to the topologically nontrivial electronic states. Also, fitting the results of superfluid density exhibited features of multiband pairing allowing the nodal gap in the electronic states which is in good agreement with the expectation of London penetration depth. The complex superconducting order parameter is suggestive of two-dimensional spin singlet or mixing singlet-triplet pairing states behind the signatures of superconductivity in CaSn 3. The mechanisms of pairing symmetry uncovered by the temperature dependence of penetration depth study of TbPdBi, FeSe and CaSn 3 meet the requirements for topological superconductivity. • For first time, topologically nontrivial pairing states of TbPdBi, Fese and CaSn 3 have been studied. • Ultra-low temperature of magnetic London penetration depth and superfluid density has been thoroughly investigated. • Superconducting gaps of these materials have also been measured. [ABSTRACT FROM AUTHOR]

Abstract: We have investigated the in-plane penetration depth, λ(T), of nominally undoped superconducting Pr2CuO4 films (T c =27.5K) by measuring the phase-sensitive millimeter-wave transmission at temperatures between 2 and 30K. The overall temperature dependence of the superfluid density, n s = λ 2(0K)/λ 2(T), resembles the behavior typical for the cuprate superconductors [n s (T)∝1− (T/T c )2]. However, a closer look on the penetration depth at low temperatures reveals flattening of its temperature dependence. We find λ(T)∝ T n with n =2.8±0.2. [Copyright &y& Elsevier]

• A new method is proposed for determining the mass of a Cooper pair. • The measurement is conducted at ultra-low temperature (10−4 K). • The London moment of a rotating spherical-shell superconductor is introduced. • Values of the Cooper-pair mass are obtained with several bulk type I superconductors. • Sample parameters are optimized to maximize the measurement precision. A new method is proposed for determining the mass of a Cooper pair at extremely low temperatures by measuring the London moment of a rotating spherical-shell superconductor. The relationship between the magnetic field generated by the rotating superconductor and the angular speed of the latter is examined. The other sample parameters are optimized to maximize the precision of the measurement. Values of the Cooper-pair mass are obtained with several bulk type-I superconductors. [ABSTRACT FROM AUTHOR]

We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a T³ power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity. [ABSTRACT FROM AUTHOR]

I discuss the process of magnetic field generation in rotating superconductors in simply connected and multiply connected geometries. In cooling a normal metal into the superconducting state while it is rotating, electrons slow down or speed up depending on the geometry and their location in the sample, apparently defying inertia. I argue that the conventional theory of superconductivity does not explain these processes. Instead, the theory of hole superconductivity does. Its predictions agree with experimental observations of Hendricks, King and Rohrschach for solid and hollow cylinders. [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]