The elevated or depressed transition temperatures observed in cuprate and pnictide superconductors and other exotic superconductors pose a challenge in the context of explaining them through the traditional Bardeen-Cooper-Schrieffer (BCS) models of superconductivity. A significant obstacle in understanding this phenomenon can be addressed by considering an alternative electron distribution. Our investigation has identified an anyonic distribution, where the occupancy of a site created by removing a hole is filled by an electron. In heavy fermion superconductors (HFSs) block spins must be included in the distribution. The interplay, that is, resonance between superconducting electrons within the conventional BCS framework and independent charge density waves (CDWs) might contribute to driving the high-transition-temperature superconductors (HTSCs).

Recently Li et al (2019 Nature 572 624) discovered a new type of oxide superconductor Nd_0.8Sr_0.2NiO₂ with T_c = 14 K. To classify superconductivity in this infinite-layer nickelate experimental upper critical field, B_c2(T), and the self-field critical current densities, J_c(sf,T), reported by Li et al (2019 Nature 572 624), are analysed in assumption of s-, d-, and p-wave pairing symmetries and single- and multiple-band superconductivity. Based on deduced the ground-state superconducting energy gap, Δ(0), the London penetration depth, λ(0), the relative jump in electronic specific heat at T_c, ΔC/C, and the ratio of 2Δ(0)/k_BT_c, we conclude that Nd_0.8Sr_0.2NiO₂ is type-II high-κ weak-coupled single-band s-wave superconductor.

The dynamic resistance is an important parameter in flux pumping. It is simple to calculate in slab geometry but more complex in tapes. In this paper another simple geometry is analysed which is a wire loop. To do this it is essential to make clear what is meant by the term 'voltage', which is ambiguous when there are alternating magnetic fields present. The term can be used if it refers to the EMF along a specified path. However this means that results are dependent on how the voltage leads are attached. If the n value of the V-I characteristic is large simple analytic expressions can be obtained. This will be referred to as the 'Bean' model solution. A more exact approach uses Faraday's law to derive a differential equation which is solved and compared with the Bean model. The dynamic resistance of the loop can be used to drive a flux pump of the type proposed by Geng and Coombs [4] and again simple expressions can be obtained for the performance. If the load is of high inductance L2 and the loop has an inductance L1 then the load current increases exponentially with a characteristic number of cycles L2/L1. The final current can be close to the critical value.

Superconductivity in highly-pressurized hydrides became primary direction for the exploration of fundamental upper limit for the superconducting transition temperature, Tc, after Drozdov et al (Nature 2015, 525, 73) discovered superconducting state with Tc=203 K in highly-compressed sulphur hydride. To date several dozens of high-temperature superconducting polyhydrides have been discovered. In addition, recently, it was reported that highly-compressed titanium and scandium exhibit record-high (up to 36 K), which is by manifold exceeded of niobium, which is the record high- ambient pressure metallic superconductor. Here we analysed experimental data on for recently discovered high-pressure superconductors (which exhibit high transition temperatures within their classes): elemental titanium (Zhang et al, Nature Communications 2022; Liu et al, Phys. Rev. B 2022), TaH3 (He et al, Chinese Phys. Lett. 2023), LaBeH8 (Song et al, Phys. Rev. Lett. 2023), and black (Li et al, Proc. Natl. Acad. Sci. 2018) and violet (Wu et al, arXiv 2023) phosphorous, to reveal the nonadiabaticity strength constant, TθTF (where Tθ is the Debye temperature, and TF the Fermi temperature) in these superconductors. The analysis showed that δ-phase of titanium and black phosphorous exhibit the Tθ/TF which are nearly identical to ones associated in A15 superconductors, while studied hydrides and violet phosphorous exhibit the constants in the same ballpark with H3S and LaH10.

The experimental data in the literature concerning the Paramagnetic Meissner Effect (PME) or also called Wohlleben effect are reviewed with the emphasis on the PME exhibited by metallic, s-wave superconductors. The PME was observed in field-cool cooling (FC-C) and field-cool warming (FC-W) m(T)-measurements on Al, Nb, Pb, Ta, in compounds like e.g., NbSe2, In-Sn, ZrB12 and others and also in MgB2, the metallic superconductor with the highest transition temperature. Furthermore, samples with different shapes like crystals, polycrystals, thin films, bi- and multilayers, nanocomposites, nanowires, mesoscopic objects and porous materials exhibited the PME. The characteristic features of the PME, found mainly in Nb disks, like the characteristic temperatures T1 and Tp and the apparative details of the various magnetic measurement techniques applied to obbserve the PME are discussed. We also show that PME can be observed with the magnetic field applied parallel and perpendicular to the sample surface, that PME can be removed by abrading the sample surface and that PME can be introduced or enhanced by irradiation processes. The PME can be observed as well in magnetization loops (MHLs, m(H)) in a narrow temperature window Tp<Tc, which enables the construction of a phase diagram for a superconducting sample exhibiting the PME. We found that the Nb disks still exhibit the PME after more than 20 years, and we present the efforts of magnetic imaging techniques (scanning SQUID microscopy, magneto-optics, diamond nitrogen-vacancy (NV)-center magnetometry, and low-energy muon spin spectroscopy, (LE-μSR)). Various attempts to explain PME behavior are discussed in detail. Especially, magnetic measurements of mesoscopic Al disks brought out important details employing the models of a giant vortex state and flux compression. Thus, we consider these approaches and demagnetization effects as the base to understand the formation of the paramagnetic signals. New directions for further experimental and theoretical analysis are also outlined.

Satterthwaite and Toepke (1970 Phys. Rev. Lett. 25 741) discovered that Th₄H₁₅-Th₄D₁₅ superhydrides exhibit superconductivity and have no isotope effect. The latter is fundamental contradiction with the concept of electron-phonon mediated superconductivity of Bardeen-Cooper-Schrieffer (BCS) theory. Soon after this work, Stritzker and Buckel (1972 Zeitschrift für Physik A Hadrons and nuclei 257 1-8) reported that superconductors in PdH_x-PdD_x system exhibit reverse isotope effect. Yussouff et al (1995 Solid State Communications 94 549) extended this finding on PdH_x-PdD_x-PdT_x system. Recent interest to hydrogen- and deuterium-rich superconductors is based on the discovery of near-room-temperature superconductivity in highly-compressed H₃S (Drozdov et al. 2015 Nature 525 73) and LaH₁₀ (Somayazulu et al 2019 Phys. Rev. Lett. 122 027001). To date, there is no clarity about isotope effect in H₃S-D₃S system, because thorough examination of available experimental data reported by Drozdov et al (2015 Nature 525 73) shows that H₃S-D₃S system perhaps has reverse isotope effect. In attempt to reaffirm/disprove our primary idea that the mechanism for near-room-temperature superconductivity in hydrogen-rich superconductors is not BCS electron-phonon interaction, we analyse the upper critical field data, B_c2(T), in Th₄H₁₅-Th₄D₁₅ phases (Satterthwaite and Toepke 1970 Phys. Rev. Lett. 25 741) and two recently discovered high-pressure hydrogen-rich phases of ThH₉ and ThH₁₀ (Semenok et al 2019 arXiv:1902.10206). As the result, it is found that all known to date thorium super-hydrides/deuterides are unconventional superconductors which have T_c/T_F ratios within a range of 0.008 < T_c/T_F < 0.120, where T_c is the superconducting transition temperature and T_F is the Fermi temperature.

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. We here study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

It has been suggested that the measured magnetic properties of hydrides under pressure claimed to be high temperature superconductors indicate that the materials are granular superconductors. Such materials will show reduced or no magnetic field expulsion under field cooling, and will trap magnetic fields when the external magnetic field is removed. They will also exhibit hysteretic behavior in magnetoresistance and other transport properties. Here we point out that hysteresis in transport properties has never been reported for hydrides under pressure. Its presence, with the expected features, would indicate that the materials trap magnetic flux, hence that they can sustain persistent currents without dissipation, something that all superconductors can do. Conversely, its absence would indicate that these materials are not superconductors.

Recently, Troyan et al (2019 arXiv:1908.01534) and Kong et al (2019 arXiv:1909.10482) extended near-room-temperature superconductors family by new yttrium superhydride polymorphs, YH_n (n = 4,6,7,9), which exhibit superconducting transition temperatures in the range of T_c = 210-243 K at pressure of P = 160-255 GPa. In this paper, temperature dependent upper critical field data, B_c2(T), for highly-compressed mixture of YH₄+YH₆ phases (reported by Kong et al 2019 arXiv:1909.10482) is analysed to deduce the ratio of T_c to the Fermi temperature, T_F. Our analysis shows that in all considered scenarios the YH₄+YH₆ mixture has the ratio 0.01 ≤ T_c/T_F ≤ 0.04. As the result, YH₄+YH₆ falls in the unconventional superconductors band in the Uemura plot. It is also found that the characteristic temperature of the order parameter amplitude fluctuations, T_fluc, in the YH₄+YH₆ mixture is only several percent above observed T_c, and thus the superconducting transition in yttrium superhydride polymorphs is fundamentally limited by thermodynamics fluctuations.

_{Superconducting foams of YBa$_2$Cu$_3$O$_y$ (YBCO) are proposed as trapped field magnets or supermagnets. The foams with an open-porous structure are light-weight, mechanically strong and can be prepared in large sample sizes. The trapped field distributions were measured using a scanning Hall probe on various sides of an YBCO foam sample after field-cooling in a magnetic field of 0.5 T produced by a square Nd-Fe-B permanent magnet. The maximum trapped field (TF) measured is about 400 G (77 K) at the bottom of the sample. Several details of the TF distribution, the current flow and possible applicatons of such superconducting foam samples in space applications, e.g., as active elements in flux-pinning docking interfaces (FPDI) or as portable strong magnets to collect debris in space, are outlined.}

We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that, despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.

The pinning force density FpJc,B=Jc×B (where Jc is the critical current density and B is the applied magnetic field) is one of the main parameters that characterize the resilience of a superconductor to carry a dissipative-free transport current in an applied magnetic field. Kramer (1973 J. Appl. Phys. 44 1360), and Dew-Hughes (1974 Phil. Mag. 30 293) proposed a widely used scaling law for the pinning force density amplitude: FpB=Fp,max×p+qp+qppqq×BBc2p×1-BBc2q, where Fp,max, Bc2, p, and q are free-fitting parameters. Since the late 1970-s till now, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb3Sn-based conductors. Godeke (2006 Supercond. Sci. Techn. 19 R68) proposed that the dependence obeys the law Fp,maxd=A×ln1d+B. However, this scaling law has several problems, for instance, the logarithm is taken from a non-dimensionless variable, and Fp,maxd&lt;0 for large grain sizes, and Fp,maxd→∞ for d→0. Here, we reanalysed the full inventory of publicly available Fp,maxd data for Nb3Sn conductors and found that the dependence can be described by Fp,maxd=Fp,max0×exp-dδ law, where the characteristic length, δ, varies within a remarkably narrow range, that is, δ=175±13 nm, for samples fabricated by different technologies. The interpretation of the result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near the 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.

As shown previously, a relation between the superconducting transition temperature and some characteristic distance in the crystal lattice holds, which enables the calculation of the superconducting transition temperature, Tc, based only on the knowledge of the electronic configuration and of some details of the crystallographic structure. This relation was found to apply for a large number of superconductors, including the high-temperature superconductors, the iron-based materials, alkali fullerides, metallic alloys, and element superconductors. When applying this scheme called Roeser-Huber formula to Moiré-type superconductivity, i.e., magic-angle twisted bi-layer graphene (tBLG) and bi-layer WSe2, we find that the calculated transition temperatures for tBLG are always higher than the available experimental data, e.g., for the magic angle 1.1∘, we find Tc≈ 4.2–6.7 K. Now, the question arises why the calculation produces larger Tc’s. Two possible scenarios may answer this question: (1) The given problem for experimentalists is the fact that for electric measurements always substrates/caps are required to arrange the electric contacts. When now discussing superconductivity in atomically thin objects, also these layers may play a role forming the Moiré patterns. The consequence of such substrate-induced super-Moiré patterns is that the resulting Moiré pattern always will show a larger cell size, and thus, a lower Tc of the final structure will result. (2) A correction factor to the Roeser-Huber formalism may be required to account for the low charge carrier density of the tBLG. Here, we test both scenarios and find that the introduction of a correction factor η enables a proper calculation of Tc, reproducing the experimental data. We find that η depends exponentially on the value of Tc.

The 11 system in iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity due to their simple structure and rich physical properties. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe1-xTex, FeSe1-xSx and FeTe1-xSx. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux, and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique.

As shown previously, a relation between the superconducting transition temperature and some characteristic distance in the crystal lattice holds, which enables the calculation of the superconducting transition temperature, Tc, based only on the knowledge of the electronic configuration and of some details of the crystallographic structure. This relation was found to apply for a large number of superconductors, including the high-temperature superconductors, the iron-based materials, alkali fullerides, metallic alloys, and element superconductors. When applying this scheme called Roeser-Huber formula to Moiré-type superconductivity, i.e., magic-angle twisted bi-layer graphene (tBLG) and bi-layer WSe2, we find that the calculated transition temperatures for tBLG are always higher than the available experimental data, e.g., for the magic angle 1.1∘, we find Tc≈ 4.2–6.7 K. Now, the question arises why the calculation produces larger Tc’s. Two possible scenarios may answer this question: (1) The given problem for experimentalists is the fact that for electric measurements always substrates/caps are required to arrange the electric contacts. When now discussing superconductivity in atomically thin objects, also these layers may play a role forming the Moiré patterns. The consequence of such substrate-induced super-Moiré patterns is that the resulting Moiré pattern always will show a larger cell size, and thus, a lower Tc of the final structure will result. (2) A correction factor to the Roeser-Huber formalism may be required to account for the low charge carrier density of the tBLG. Here, we test both scenarios and find that the introduction of a correction factor η enables a proper calculation of Tc, reproducing the experimental data. We find that η depends exponentially on the value of Tc.

An innovative superconducting mechanism was developed based on a patented discovery of room temperature superconductivity in several thorium (Th) salts or compounds. The rationale behind this discovery is through the experimental results about the unique electrical and magnetic properties of these Th salts. Accordingly, this new superconducting mechanism for these Th salts was obtained through the analyses of the compounds’ molecular configurations and the packings of their relevant crystal structures. Owing to the distinctive properties of the Th compounds in this discovery, we further established a different electron pairing scheme as opposed to the pairing of the Cooper pairs. Compared to the long distance electron pairing of the Cooper pairs, the new electron pairing in our mechanism is constructed by two closely correlated electrons that reside on the same atomic orbital of the Th cation as an electron lone pair. In this new superconducting mechanism, the Th cation is sitting on a relevant crystallographic lattice arrangement or a network of the relevant Th compounds. This network is constructed by many Th cations along certain crystallographic lattice arrangement where each Th cation contains one electron lone pair. This network allows the electron lone pairs on the Th cations to be delocalized over the network, “in pair”, and thus, reveals the electron lone pair in presence in a long distance fashion. The closely correlated electron lone pairs hop on this network and thus, construct the supercurrent over the network. This explanation about the superconductivity laid the basis for our superconducting mechanism. All these conclusions came from the previous studies about these compounds that illustrated their unusual features of a coexistence of high electrical conductivity and diamagnetism. These electrical and magnetic properties fall in line with that of superconductors but, surprisingly, these Th compounds have such properties at the ambient condition, meaning under room temperature and atmosphere pressure. We expect that this mechanism may be appropriate to be utilized to other superconducting cases and therefore, can be adapted to describe the superconducting phenomenon for other superconductors.

Real-time evolution of the electron densities under excitations in La₂CuO₄ was calculated by the time-dependent density functional theory (TDDFT). The author found, for the first time, under excitations, the electron cloud of Cu²⁺ changes obviously and the characteristic frequencies are 83 meV and 36 meV, respectively, for two different modes. The results are unexpected and close to that of lattice vibrations. The results show that the electron cloud of Cu²⁺ (just like the lattice) can be the electron-pairing medium in high temperature copper oxide superconductors.

Nickelate superconductors, R1-xAxNiO2 (where R is a rare earth metal and A = Sr, Ca), experimentally discovered in 2019 exhibit many unexplained mysteries as the existence of a superconducting state with Tc (up to 18 K) in thin films and its absence in bulk materials. Another unexplained mystery of nickelates is their temperature-dependent upper critical field, Bc2T, which can be nicely fitted to two-dimensional (2D) models; however the deduced film thickness, dsc,GL, exceeds the physical film thickness, dsc, by a manifold. To address the latter, it should be noted that 2D models assume that dsc is less than the in-plane and out-of-plane ground state coherence lengths, dsc&lt;ξab0 and dsc&lt;ξc0, respectively, and, in addition, that the inequality ξc0&lt;ξab0 satisfies. Analysis of the reported experimental Bc2T data showed that at least one of these conditions does not satisfy for R1-xAxNiO2 films. This implies that nickelate films are not 2D superconductors, even despite though that the superconducting state is observed only in thin films. Based on this, here we proposed analytical three dimensional (3D) model for global data fit of in-plane and out-of-plane Bc2T in nickelates. The model is based on a heuristic expression for temperature dependent coherence length anisotropy: γξT=γξ01-1a×TTc, where a&gt;1 is a unitless free-fitting parameter. The proposed expression for γξT, perhaps, has a much broader application because it has been successfully applied to bulk pnictide and chalcogenide superconductors.

We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A energy processes such as the classical heat engines, apparently well follow the second law of thermodynamics; Type B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to do useful work in driving ATP synthesis, which follows the first law of thermodynamics (conservation of mass and energy) but does not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric-function-gated isothermal electricity and epicatalysis have been created through human efforts. The innovative efforts on Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for the humanity on Earth.

The part of this article dealing with topological insulators and topological superconductors was first written about two years ago - the ideas in the part about the topological universe originated six years ago or more. It’s rather strange that I never put the two parts together in writing before. My belief in unification is unshakeable - I’ve been convinced for years that the universe must be composed of topology. Since Earth is part of the cosmos, entanglement means it must have topological materials. The reverse is also true: topological materials on Earth are well known to science - so in a unification, space and time inevitably possess topological composition. Topological materials (topological insulators, topological superconductors) can be less mystifying if they’re related to the paradigm-shifting deterministic view of quantum mechanics which is described in the universal topology (the “rubber-sheet geometry” of the cosmos): see my previous submission “Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories" at https://www.preprints.org/manuscript/202105.0239/v1 (the first section of this present article is a quick summary of the relevant parts).