Superconductivity is a phenomenon in which a material exhibits zero electrical resistance and perfect diamagnetism through the Meissner effect when cooled below its critical temperature. In type-II superconductors, critical magnetic field parameters, including Hc1H_{c1}Hc1, Hc2H_{c2}Hc2, and HirrH_{\mathrm{irr}}Hirr, play essential roles in determining the stability of the superconducting phase under external magnetic fields. This review discusses the relationship among the Meissner effect, critical magnetic fields, magnetic vortices, flux pinning, synthesis methods, and the applications of high-temperature superconductors (HTSs), particularly YBCO and BSCCO. The reviewed studies indicate that microstructure, doping, and crystal quality strongly influence critical magnetic field performance and superconducting stability. However, previous studies have generally examined the Meissner effect and critical magnetic fields separately. Therefore, a more comprehensive review is needed to integrate recent developments in the theory, experimental investigation, and applications of modern superconductors.
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