A mechanism for nonmonotonic Tc,max(n) in multilayer cuprates

I propose an explanation of the observed dependence of the maximal critical temperature Tc,max on the number of conducting layers n in layered copper-oxide superconductors within the preformed pair mechanism. Copper-oxygen planes fine-tune the lattice anisotropy and regulate the balance between the attractive and kinetic energies of carrier holes. To maximize the Bose-Einstein condensation temperature, real-space pairs must be compact and light at the same time. Generally, Tc,max increases between n = 1 and n = 3 because pairs become lighter. For n > 3, the rising kinetic energy weakens the pairs, leading to inflated pair volumes and reduced Tc,max. By varying model parameters, the peak of Tc,max(n) can be tuned to n = 2, n = 3, or n > 3. I will also discuss strategies for using this knowledge to boost Tc,max beyond the current record of 138 K.