Abstract:
A topical overview on the state of the art and science of superconducting materials is presented. The relation of atomic structure and suggested superconductivity mechanisms as well as possible applications are discussed for the various families of superconducting materials discovered within the last 25 years.

Abstract:
We describe the phenomenon of generation of an external field of forces from piezoelectric materials subjected to the application of electric fields or mechanical stress. We show that piezoelectric materials are capable of producing nonlocal forces of induction in external objects and we conclude that the nature of the forces generated is not originated from traditional interactions. Further we specifically assert that the generation of forces by the piezoelectric materials is ruled by the hypothesis of preexisting condition of generalized quantum entanglement between the molecular structure of the material bulk and the surrounding environment. In addition, the widely spread coupling of the molecules with the environment can be manifested from the so-called direct effect or the converse effect in piezoelectric materials and this coupling is not intermediated by acoustic waves or electromagnetic fields. We show that the novel effect has a theoretical explanation consistent with the generalized quantum entanglement framework and the direction of the induced forces depends on either the direction of the mechanical force or the electric field applied in these materials.

Abstract:
We show that exact results are obtained for the calculation of Casimir forces between arbitrary materials using the concept of surface impedances, obtaining in a trivial way the force in the limit of perfect conductors and also Lifshitz formula in the limit of semi-infinite media. As an example we present a full and rigorous calculation of the Casimir force between two metallic half-spaces described by a hydrodynamic nonlocal dielectric response.

Abstract:
The extensive ab initio total energy calculations using the VASP-PAW method with the generalized gradient approximation (GGA) for the exchange-correlation potential are applied to systematic investigation of structural, electronic and magnetic properties in quaternary oxybismuthides LaOMBi (where M = Sc, Ti...Ni, Cu). The energy spectrum features similar to lanthanum-iron oxyarsenide LaOFeAs and non-magnetic ground state are indicative of superconductivity possible in lanthanum-nickel oxybismuthide LaONiBi.

Abstract:
In this work we present a theoretical explanation for the possible anomalous forces induced by superconducting disks and toroids, based on the hypothesis of a preexisting state of generalized quantum entanglement that can produce momentum variation exchanged between Cooper pairs and outer particles. Considering the immense amount of particles involved in the phenomenon as coherent Cooper pairs, and indications of previous studies, we use classical quantities as macroscopic observables in our calculations. We here analyzed the behavior of such superconductors and compared the experimental results early obtained in the literature with our theoretical proposal. We found that the theoretical calculations agreed with very good accuracy for two different experiments and devices. The present work really highlights the possibility of superconducting materials to be applied to induce outer forces in the environment and in external objects, as explained by our theoretical model.

Abstract:
We consider dislocations in the framework of Eringen's nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All classical singularities of the Peach-Koehler forces are eliminated. The extremum values of the forces are found near the dislocation line.

Abstract:
Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modelled and analyzed. The formalism is based on the Maxwell equations, and a material current-voltage characteristics, linear for normal metals, and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function source-field turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain, in both Fourier and real space. Next, the dynamical behaviour of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic avalanches. The avalanches tend to invade the central part where the density of trapped flux is largest, forming dendritic patterns in excellent agreement with magneto-optical images. Detailed profiles of current and flux density are presented and discussed. Finally, the formalism is extended to multiply connected samples, and numerical results for a patterned superconducting film, a ring with a square lattice of antidots, are presented and discussed.

Abstract:
Motivated by recent experiments on nonlocal transport through multiterminal superconducting hybrid structures, we present self-consistent calculations based on quasiclassical Green's functions for the order parameter, currents and voltages in a system consisting of a diffusive superconductor connected to two normal and one superconducting electrodes. We investigate non-equilibrium effects for different biasing conditions corresponding to measurements of the nonlocal conductance and of the nonlocal resistance. It is shown that while the nonlocal conductance does not change its sign, this change might be observed in a nonlocal resistance measurement for certain parameter range. The change of sign of the nonlocal signal takes places at a voltage of the order of the self-consistent gap of the superconducting region. We show that this is not related to the nonlocal Andreev processes but rather to non-equilibrium effects. We finally discuss the case of four terminal measurements and demonstrate that a change of sign in the nonlocal resistance appears when the current injected into the superconductor exceeds a critical value. The connection to the existing experiments is discussed.

Abstract:
We report in the present work a novel effect associated with deviations of laser beams when in the surroundings there is a piezoelectric ceramic subjected to high voltages. In our previous work we presented experimental evidences of the generation of forces at distance by piezoelectric materials. Hence a methodology for remote sensing and metrology which enhanced the weak effects of the property of generalized quantum entanglement was proposed. The preexisting state between all existing particles in physical systems can allow that piezoelectric ceramics induct forces at distance detected by a sensible accelerometer apart without involving any known local interaction such as those of acoustic or electromagnetic nature. Motivated by the results, we proceed and discover that new unprecedented visual effects arise when nonlocal forces generated by a piezoelectric ceramic change the laser beam profiles even considering its weakness. This novel effect seems to be really detected in our experiments and this achievement opens one opportunity more for developing new technological applications.

Abstract:
Recently, the search for Majorana fermions (MFs) has become one of the most important and exciting issues in condensed matter physics since such an exotic quasiparticle is expected to potentially give rise to unprecedented quantum phenomena whose functional properties will be used to develop future quantum technology. Theoretically, the MFs may reside in various types of topological superconductor materials that is characterized by the topologically protected gapless surface state which are essentially an Andreev bound state. Superconducting doped topological insulators and topological crystalline insulators are promising candidates to harbor the MFs. In this review, we discuss recent progress and understanding on the research of MFs based on time-reversal-invariant superconducting topological materials to deepen our understanding and have a better outlook on both the search for and realization of MFs in these systems. We also discuss some advantages of these bulk systems to realize MFs including remarkable superconducting robustness against nonmagnetic impurities.