On superconductivity in (YBa2Cu3O7−δ)m/(PrBa2Cu3O7−δ)n superlattices. A quantitative analysis based on indirect-exchange pairing

We undertake a theoretical analysis of critical temperatures TC(m,n) observed in superlattices composed of m YBa2Cu3O7−δ (YBCO) and, or alternating with, n PrBa2Cu3O7−δ (PrBCO) unit cells, as a function of m and n. A survey of suggested explanations, and of different phenomenological analyses based on Kosterlitz–Thouless transitions, proximity effects, and charge transfer processes, shows that no conclusive interpretation of these phenomena exists. Instead, we adopt a microscopic approach based on indirect-exchange Cooper pairing between conduction electrons (quasi-particles) via oxygen anions. On this basis, and due to structural and electronic similarities between the components, an (m,n) YBCO/PrBCO supercell is treated as an “extended” YBCO system. Assuming that only the YBCO unit cell adjacent to PrBCO is (electronically) directly affected upon forming an (m,n) supercell, essential agreement with experiment is obtained for all values of m and n, without any parameter adjustment. In conformity with the results of conductance experiments by Cieplak et al. (Phys. Rev. B 50 (1994) 12876) we establish a direct correlation between TC(m,n) and a normal-state property of the system, the Fermi vector length kF, as a function of m and n. The results do not support the (widespread) assumption of interlayer (intercell) coupling in the YBCO system, neither between different m-YBCO units nor intercell coupling within the same unit.