Superconductivity and the quasiparticle mass enhancement near the charge density wave critical point using the Bethe-Salpeter method: Application to cuprates

In recent years, charge-channel order in strongly correlated metals has attracted much attention. Representative examples include electronic nematic order in cuprates and iron-based superconductors, and Star-of-David order in kagome metals. Critical phenomena and unconventional superconductivity arising from fluctuations of such charge-channel orders are central issues today; however, the essential role is played by many-body effects (vertex corrections) beyond the mean-field approximation, and their origin and computational methods have not been established. In this study, we propose the Bethe-Salpeter equation method to evaluate electron-electron interactions in two-dimensional Hubbard models beyond the mean-field approximation. Based on the Baym-Kadanoff conserving approximation, we find that an attractive interaction in the charge channel emerges from the Aslamazov-Larkin vertex corrections that describe the interference processes among spin fluctuations. Applying this method to the square-lattice Hubbard model shows that the cooperation of attractive charge fluctuations and repulsive spin fluctuations yields high-${T}_{c} d$-wave superconductivity together with enhanced effective mass. These results provide a natural explanation for the phase diagram of cuprate superconductors, in which $d$-wave superconductivity is strongly enhanced near the charge-order critical point. The theory can also be applied to iron-based and nickelate superconductors, suggesting broad potential for future applications.