Quarter-filled systems with frustration: Candidate for correlated electron superconductivity*

A necessary condition for superconductivity (SC) driven by electron correlation is that electron electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the non-interacting limit. We present the results of high-precision calculations of superconducting pair-pair correlations on four different frustrated lattices over the complete range of carrier density $0 < \rho < 1$ in each case. We find that pair correlations are enhanced relative to the noninteracting limit only for density $\rho$ equal to or close to $0.5$ ($1/4$ filling). At all other $\rho$ pair correlations are suppressed by interactions. This enhancement is due to the proximity to a spin-gapped paired-electron crystal (PEC) state that occurs at $\rho=0.5$. Our theory explains the pseudogap observed at high temperatures in many organic superconductors. The remarkable bandfilling specificity is an essential ingredient to understanding the mechanism of superconductivity in the two-dimensional organic charge-transfer solids as well as the many different families of other unconventional superconductors that share this bandfilling.