A Space-Time Study of the Electron-Electron Interaction in High-TC Parent Compound La2CuO4: In Search of an Attractive Effective Interaction

Abstract: The superconductivity under doping in the famous cuprate compounds is believed to originate in the CuO2 planes. The mediator of pairing is generally accepted to be induced from electronic degrees of freedom. While many mechanisms, such as spin fluctuations, have been proposed throughout the years, little research has been carried out on the role of the retarded attraction due to electronic overscreening. In this study, the dynamically screened interaction W(r,r';t) is studied in the CuO2 planes of the parent compound La2CuO4. To this end, a repulsive test charge, representing an electron, is introduced at various r' in the CuO2 plane, and W(r,r';t) is calculated as a function of r and t. The aim is to explore the possibility of the existence of an attractive effective interaction between electrons. The static screened interaction W(r,r';ω=0), which is the time average of W(r,r';t) is also studied. In addition, the effective interactions U1(r,r';t) and U3(r,r';t), corresponding to the well-known one- and three-band models, are investigated using the constrained random-phase approximation (cRPA). Substantial regions of the CuO2 plane do indeed exhibit an attractive effective interaction, with both U1 and U3 being negative. On the other hand, the extent of such regions is significantly smaller in SrVO3, a non-superconducting metal. The present work suggests that future studies of electronic overscreening as a possible pairing mechanism is worth consideration. The same ab initio parameters as obtained and utilized in this work can be used to construct a Hubbard-Holstein model, within which the gap function can be calculated by solving the Eliashberg equations.