Doping-dependent effective Hubbard interactions for cuprate superconductors

Nonlocal Coulomb interactions can significantly affect the electronic correlations in (quasi-)two-dimensional materials. Based on a variational principle, we derive effective Hubbard model descriptions to capture electronic correlations even in the presence of nonlocal Coulomb interactions. For square lattice systems like the cuprate superconductors, we calculate the effective on-site repulsion U* using the Dynamical Cluster Approximation (DCA) as function of doping, interaction strength and temperature. We find a pronouced reduction of U* in the doped regime compared to the half-filled case. In other words, Hubbard based modelling of cuprate superconductors should involve doping-dependent effective interactions U*.