Increasing the critical temperature of superconducting materials, particularly the goal of achieving room temperature, remains one of the significant challenges in the field. Addressing this challenge requires a comprehensive understanding of the factors influencing critical temperature. Specifically, it is hypothesized that increasing the interlayer distance between \(CuO_2\) planes, along with a corresponding reduction in the surface area of these planes or an increase in the c/a ratio of the crystal lattice constants, could elevate the critical temperature of high-temperature cuprate superconductors. In this study, we investigate the relationship between critical temperature and the c/a ratio at various doping levels of the single \(CuO_2\) layer cuprate superconductor \(Hg{Ba}_{2}Cu{O}_{4+\delta }\) (Hg-1201), which exhibits the highest known critical temperature, under both atmospheric and high-pressure conditions. Our results indicate no significant correlation between critical temperature and the c/a ratio under atmospheric pressure. However, under applied external pressure, we show a generally decreasing critical temperature as a function of the c/a ratio. These findings suggest that parameters related to the \(CuO_2\) planes in Hg-1201 and other high-temperature cuprate superconductors are insufficient to explain the variations in critical temperature. Furthermore, we conclude that charge reservoirs, carrier dynamics, and inter-electronic orbital interactions significantly influence the fluctuations in critical temperature.
