A necessary condition for superconductivity (SC) driven by electron correlations is that electron-electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the noninteracting limit. We report high-precision numerical calculations of the ground state within the frustrated two-dimensional (2D) Hubbard Hamiltonian for a wide range of carrier concentration ρ (0 < ρ < 1) per site. We find that long range superconducting pair correlations are enhanced only for ρ 0.5. At all other fillings e-e interactions mostly suppress pair correlations. The enhancement of pair correlations is driven by the strong tendency to local singlet bond formation and spin gap (SG) in ρ = 0.5, in lattices with quantum fluctuation [1][2][3] . We also report determinantal quantum Monte Carlo (DQMC) calculations that are in strong agreement with our ground state results. Our work provides a key ingredient to the mechanism of SC in the 2D organic charge-transfer solids (CTS), and many other unconventional superconductors with frustrated crystal lattices and ρ 0.5, while explaining the absence of SC in structurally related materials with substantially different ρ.The possibility that e-e interactions can be the driving force behind SC in correlated-electron systems has been intensely investigated since the discovery of SC in the high T c cuprates. The minimal requirements for a complete theory are, (i) the superconducting pair correlations are enhanced by e-e interactions, and (ii) pair correlations are long range. For moderate to large e-e interactions, pair correlations are perhaps best calculated numerically, which however can be done only for finite clusters. The simplest model incorporating e-e interactions is usually assumed to be the Hubbard model, which in quite general form can be written asAll terms in Eq. 1 have their standard meaning. The first sum is the kinetic energy of noninteracting electrons within a 2D tight-binding model with hopping matrix elements t ij ; U and V ij are onsite and nearest neighbor (n.n.) Coulomb interactions respectively. Existing numerical calculations within Eq. 1 on 2D lattices have failed to find enhancement of pair-pair correlations relative to the noninteracting model without making severe approximations 4 . It has sometimes been surmised that correlated-electron SC might evolve upon doping a spin-gapped semiconductor, as would occur in toy models such as a 2D lattice consisting of weakly coupled even-leg ladders 5,6 . Finding realistic 2D models with SG and enhanced pair correlations however remains challenging. In the present work we demonstrate from explicit numerical calculations on frustrated 2D lattices enhanced pair correlations evolving from a spin-gapped state at a carrier density ρ 0.5, far from the region most heavily investigated until now (0.7 < ρ < 1.0). We further point out the strong relevance of the resulting theoretical picture to real materials, in particular the 2D CTS superconductors, which were discovered earlier than the cuprates 7 but are still not un...

We present the results of precise correlated-electron calculations on the monomer lattices of the organic charge-transfer solids κ-(BEDT-TTF)2X for 32 and 64 molecular sites. Our calculations are for band parameters corresponding to X = Cu[N(CN)2]Cl and Cu2(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 chargetransfer 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.