The two-band hybridized superconductor which the pairing occurred by conduction electron band and other-electron band are considered within a mean-field approximation. The critical temperature, zero-temperature order parameter, gap-to-Tcratio, and isotope effect coefficient are derived. We find that the hybridization coefficient shows a little effect on the superconductor that conduction electron band has the same energy as other-electron band but shows more effect on the superconductor that conduction electron band coexists with lower-energy other-electron band. The critical temperature is decreased as the hybridization coefficient increases. The higher value of hybridization coefficient, lower value of gap-to-Tcratio, and higher value of isotope effect coefficient are found.

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In this research, we investigated the gap-to-[Formula: see text] ratio of LaH[Formula: see text] and LaD[Formula: see text] superconductors by using modification of the BCS theory. The assumption of carriers under high pressure was in a new state, revealing a novel dispersion relation and providing a peak located in density of state. The precise formula of the gap-to-[Formula: see text] ratio was derived and achieved. The numerical results were examined, and subsequently a greater value than the one in the BCS was obtained. Our gap-to-[Formula: see text] results showed the best fit with the first-principle calculation of LaH[Formula: see text] ([Formula: see text]–5.25) and LaD[Formula: see text] ([Formula: see text]–5.20) superconductors. Finally, those results were carried out to the gap-to-[Formula: see text] ratio of metal-hydrides such as H3S, CaH6, YH4, YH6, YH7, YH9, CeH9, CeH[Formula: see text], ThH9 and ThH[Formula: see text] yielding the positive outcome and interpretation.

The aim of this research is to study the critical temperature depending on the pressure of one-band superconductor. We derive the exact equation of the critical temperature [Formula: see text] by using the BCS-like model. The effect of pressure and pseudogap on critical temperature has been investigated. The analytic form and the approximation of the critical temperature are shown. First, we consider the effect of pressure on the critical temperature and find that the critical temperature increased as pressure is increased which fits well with the experimental data of Tl-based and Bi-based superconductors. Second, the effect of the pseudogap on the critical temperature is considered. We found that the critical temperature is decreased as pressure increased which agrees to the data of [Formula: see text], the iron chalcogenides [Formula: see text], intermetallic compounds [Formula: see text] and [Formula: see text] superconductors.