According to our theory, Bose–Einstein condensation is established only up to the remaining virtual energy band gap i.e., in the absence of a finite band gap energy associated with normal-state electrons, no superconducting condensation should be possible. In terms of the Fermi surface diagrams, the normal-state electrons above the Fermi energy level in the superconducting system descend towards the band gap to fill the energy levels from zero up to the Fermi level, thereby forming a superconducting gap above the Fermi level to bring about the resistance-free state. Figure 3 illustrates that the band gap tends to zero in the superconducting state when the Bose–Einstein condensation is found to replace the virtual energy band gap. Even good conductors have a negligibly small bandgap in our model. Non-crystalline amorphous silicon has a band gap, which contradicts the conventional belief that band gaps are induced by crystalline periodic potential. If V = U B C S + U c > 0, the superconducting gap becomes zero, even though the band gap is nonzero. In conclusion, band gaps originate from phonon-mediated BCS-type repulsive electron–electron interactions and Coulomb repulsions. Conventional theories calculate band gaps by applying a model with standing wave-like wave functions, either by applying Bragg diffraction or another scheme that makes use of periodic Bloch wave equations. This postulate has not yet been confirmed. Although we are satisfied with the assumption itself, the superconducting electrons and the normal-state electrons of finite resistance act in a parallel circuit connection to make the total resistance of the circuit tend to zero. Furthermore, for superconductors in general, we have no clear explanation of why the remaining normal electrons show no resistance. Therefore, for high-temperature superconductors with transition temperatures above 40 K, we generally require either a restructured BCS theory or a different theoretical basis altogether. As shown by McMillan, strong interactions can give rise to low-temperature superconductors up to a maximum highest superconducting transition temperature of around 30 K. Poor metals comprise most low-temperature superconductors, while it is doping in insulators that is found to explain most high-temperature ones. Some theoretical approaches to HTSCs are still under development, in a Heisenberg antiferromagnetic model that uses the formalism of Green’s function and in the attractive Hubbard model, which makes use of dynamical mean field theory. However, the linear dependence of resistivity on temperature, the very high superconducting transition temperatures, and the origin of the pseudo-gap, among other things, all still require clearer explanations if a full consensus is to be achieved on a theoretical model for HTSCs. One important characteristic of high-temperature superconductors (HTSCs) is the existence of CuO 2 planes in their structures. However, many theoretical models have been proposed. In contrast, the discovery in 1986 of high-temperature superconductivity has not yet been fully accepted and acknowledged by theoreticians, and debates about this have been introduced. Ionic intervention was therefore confirmed to be the experimental observation of the isotope effect, providing strong evidence in support of the BCS model. The mechanism was derived from electron–electron interactions mediated by lattice ions where this indirect interaction exceeds direct Coulomb interaction, such that the repulsive Coulomb interaction is overcome, thereby causing attraction to occur. Following the discovery of superconductivity by Onnes, the phenomenon could be described quite well for low temperatures by Bardeen–Cooper–Schrieffer (BCS) theory. The conventional properties of superconductors different from normal materials are classified as no resistance below a critical temperature and no magnetic field inside bulk.
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