Towards predictive ab initio methods for unconventional superconductivity: a study of multilayer cuprates.

High-temperature n-layer cuprate superconductors have the remarkable universal feature that the maximum transition temperature T_C is always obtained for the tri-layer compound. It remains unclear how the recent breakthroughs [1,2], highlighting the relation of the charge transfer gap (CTG) and the spin-exchange J with the pairing density, can be related to this universality. By integrating an exact diagonalization solver to a density functional theory plus cluster dynamical mean-field theory framework [3], we carry unprecedented charge self-consistent calculations for n=1-5 multilayer cuprates. Remarkably, the undoped compounds already host a peculiar behavior as a function of n: the CTG first decreases until reaching a minimum at n=3, and then stabilizes. The CTG is smaller in the inner CuO₂ planes, and consequently the spin exchange J is larger as compared to the outer planes, which corroborates the experimental evidence of stronger antiferromagnetic spin fluctuations in the inner planes. Most importantly, our work paves the way towards ab initio material-specific predictions of the superconducting order parameter.

[1] N. Kowalski et al., PNAS 118 (2021)

[2] S. M. O’Mahony et al., PNAS 119 (2022)

[3] K. Haule et al., PRB 81 (2010)