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Coulomb enhancement of superconducting pair-pair correlations in a $\frac{3}{4}$-filled model for $κ$-(BEDT-TTF)$_2$X

We present the results of precise correlated-electron calculations on the monomer lattices of the organic charge-transfer solids $κ$-(BEDT-TTF)$_2$X for 32 and 64 molecular sites. Our calculations are for band parameters corresponding to X = Cu[N(CN)$_2$]Cl and Cu$_2$(CN)$_3$, which are semiconducting antiferromagnetic and quantum spin liquid, respectively, at ambient pressure. We have performed our calculations for variable electron densities $ρ$ per BEDT-TTF molecule, with $ρ$ ranging from 1 to 2. We find that $d$-wave superconducting pair-pair correlations are enhanced by electron-electron interactions only for a narrow carrier concentration about $ρ=1.5$, which is precisely the carrier concentration where superconductivity in the charge-transfer solids occurs. Our results indicate that the enhancement in pair-pair correlations is not related to antiferromagnetic order, but to a proximate hidden spin-singlet state that manifests itself as a charge-ordered state in other charge-transfer solids. Long-range superconducting order does not appear to be present in the purely electronic model, suggesting that electron-phonon interactions also must play a role in a complete theory of superconductivity.