Even after decades of research, the microscopic mechanism of cuprate superconductivity remains disputed. Recent work suggests that many of the unusual properties of high-temperature superconductors can be explained by considering an additional forward-scattering interaction treated in the dimensional reduction formalism [1,2]. However, current analytical calculations are restricted to s-wave symmetry, which cannot explain the d-wave nature of cuprates. In this poster, I will present the previously developed method of dimensional reduction and extend it to account for the anisotropic d-wave nature of the cuprates. I will also show explicit calculations for a finite-range interaction mediated by B1g optical phonons. It is expected that this method can be used to calculate the superconducting phase diagram with respect to temperature and doping across different cuprates and the corresponding isotope exponent. This will provide a strong test of forward-scattering physics in cuprates.

[1] Dmitry Miserev et al. “High-Temperature Superconductivity from Finite-Range Attractive Interaction”. In: Phys. Rev. Lett. 135 (18 Oct. 2025)

[2] Joel Hutchinson et al. Introduction to dimensional reduction of fermions. 2025. arXiv: 2504.01670