Correlating the charge-transfer gap to the maximum transition temperature in Bi 2 Sr 2 Ca n -1 Cu n O 2 n +4+δ .

As the number of CuO layers, , in each unit cell of a cuprate family increases, the maximum transition temperature () exhibits a universal bell-shaped curve with a peak at = 3. The microscopic mechanism of this trend remains elusive. In this study, we used advanced electron microscopy to image the atomic structure of cuprates in the BiSrCaCuO family with 1 ≤ ≤ 9; the evolution of the charge-transfer gap size (Δ) with can be measured simultaneously. We determined that the dependence of Δ follows an inverted bell-shaped curve with the minimum Δ value at = 3. The correlation between Δ, , and may clarify the origin of superconductivity in cuprates.