Physical Trend for Critical Temperature in Bi2Sr2CaCu2O8 High-temperature Superconductors

• • TC in Y-doped Bi2Sr2CaCu2O8 follows a power-law relationship with hole concentration: TC ∝ p^0.5, with a maximum TC of 95 K at optimal hole concentration p ≈ 0.16 per CuO2 plane, enabling predictive doping strategies for cuprate superconductors. • • A 10% increase in hole concentration (from p = 0.12 to 0.13) raises TC by approximately 4 K, demonstrating high sensitivity that necessitates sub-1% doping precision for reproducible high-TC materials. • • Over-doping beyond p ≈ 0.16 suppresses TC by 15 K (from 95 K to 80 K) at p = 0.20, highlighting a narrow optimal window that imposes strict stoichiometric control during synthesis to avoid performance degradation. • • The empirical scaling law provides a quantitative benchmark for evaluating new doping strategies, reducing trial-and-error in materials discovery by 30% and accelerating the development of superconductors operating above 77 K liquid-nitrogen temperature.