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.

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.

Struts of a superconducting YBa2Cu3Oy (YBCO) foam prepared by the infiltration growth method on the base of commercial polyurethane foams were extracted from the bulk, and thoroughly characterized concerning the microstructure and the magnetoresistance, measured by the four-point technique. Optical microscopy, electron microscopy, electron backscatter diffraction and atomic force microscopy observations indicate an unique microstructure of the foam struts which shows a large amount of tiny Y2BaCuO5 (Y-211) particles (with diameters between 50–100 nm) being enclosed in channel-like grain boundaries between the YBCO grains and an one-of-a-kind surface of the struts covered with Ba3Cu5Oy-particles. The resistance data obtained at temperatures in the range 4.2 K ≤T≤ 150 K (applied magnetic fields ranging from 0 to 7 T) were analyzed in the framework of the fluctuation-induced conductivity (FIC) approach using the Aslamazov-Larkin model. The resulting FIC curves reveal the presence of five distinct fluctuation regimes, namely, the short-wave (SWF), one-dimensional (1D), two-dimensional (2D), three-dimensional (3D), and critical (CR) fluctuation domains. The analysis of the FIC data enable the coherence length in the direction of the c-axis at zero-temperature (ξc(0)), the lower and upper critical magnetic fields (Bc1, Bc2), the critical current density at T= 0 K (Jc(0)) and several other parameters describing the the material’s superconducting properties to be determined. The present data reveal that the minuscule Y-211 particles found along the YBCO grain boundaries alter the excess conductivity and the fluctuation behavior as compared to conventional YBCO samples, leading to a quite high value for Jc(0) for a sample without added flux pinning centers.

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.

Superconducting YBa2Cu3Oy (YBCO) foams were prepared using commercial open-cell, polyurethane foams as starting material to form ceramic Y2BaCuO5 (Y-211) foams which are then converted into superconducting YBCO by using the infiltration growth process. For modelling the superconducting and mechanical properties of the foam samples, a Kelvin-type cell may be employed as a first approach like done in the literature for pure polyurethane foams. However, for a refined model of a superconducting foam sample, the real sample structure must be considered. Thus, a proper description of the specific microstructure of the superconducting YBCO foams is required. A variety of parameters including the cell size and shape, the window size and shape, the length and shape of the foam struts or ligaments and the respective angles of intersection are used to describe the real foam structure. To obtain a set of reliable data, YBCO foam samples were investigated using optical microscopy, SEM and electron backscatter diffraction (EBSD). The detailed investigation of the foam microstructure reveals not only the differences to the polymeric foams used as base material, but also gives insight to details of the infiltration growth process via the increased surface amount in a foam sample.

_{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.}