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 2 layers, n , in each unit cell of a cuprate family increases, the maximum transition temperature ( T c,max ) exhibits a universal bell-shaped curve with a peak at n = 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 Bi 2 Sr 2 Ca n -1 Cu n O 2 n +4+δ family with 1 ≤ n ≤ 9; the evolution of the charge-transfer gap size (Δ) with n can be measured simultaneously. We determined that the n dependence of Δ follows an inverted bell-shaped curve with the minimum Δ value at n = 3. The correlation between Δ, n , and T c,max may clarify the origin of superconductivity in cuprates.