Atomic and bond polarization causing strong screening of short-range Coulomb interactions and its effect in cuprate superconductors

We present a novel and efficient real space, semiclassical model of electric polarization with general applicability to any system in which screening plays an important role. This model includes the effects of both atomic and bond polarizabilities, the latter originating from the modification of local bond charge transfer energies induced by polarizing charges. The nonlinear interference of multiple polarization clouds and the emergence of local field effects are highlighted as key phenomena highly influencing the short-range screening of the Coulomb interaction. As a representative system to showcase this model, the screened interaction between doped holes in the CuO$_2$ planes of cuprate high-temperature superconductors is investigated. This leads to the emergence of striking direction-dependent short-range minima in their Coulomb repulsion, which can strongly reduce the need for retardation effects and allow for an enhancement of the attractive interaction resulting from the exchange of bosons between two electrons or holes. This in turn enhances T$_C$, shortens the Cooper pair coherence length and supports the materialization of the pseudogap phase anisotropy observed in many high-T$_C$ superconductors.