Electronic Energy Levels in High-Temperature Superconductors

Parent materials of high-temperature superconductors (HTSC) need to be doped to become superconducting. The optimum doping for maximum critical transition temperature T _c has been analyzed for more than 20 materials. Assuming a uniform doping distribution the distance x between doped unit cells—projected into the CuO₂ plane for cuprates—shows a strong linear correlation to the inverse of T _c in the form (2x)²=m ₁1/T _c with a slope of m ₁=(2.786±0.029)×10⁻¹⁵ m² K. The mercury cuprate homologous series HgBa₂Ca _n−1Cu _n O_2n+2+δ with n=1,2,3 has been used to demonstrate the procedure deriving the doping distance x from the optimum doping value δ.