Coulomb enhancement of superconducting pair-pair correlations in a34-filled model forκ−(BEDT-TTF)2X

We present the results of precise correlated-electron calculations on the monomer lattices of the organic charge-transfer solids $\ensuremath{\kappa}\text{\ensuremath{-}}(\text{BEDT-}{\mathrm{TTF})}₂X$ for 32 and 64 molecular sites. Our calculations are for band parameters corresponding to $X=\text{Cu}[\mathrm{N}{(\mathrm{CN})}₂]\mathrm{Cl}$ and ${\mathrm{Cu}}₂({\mathrm{CN})}₃$, which are semiconducting antiferromagnetic and quantum spin liquid, respectively, at ambient pressure. We have performed our calculations for variable electron densities $\ensuremath{\rho}$ per BEDT-TTF molecule, with $\ensuremath{\rho}$ 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 $\ensuremath{\rho}=1.5$, 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.