Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the $\beta$, ${\beta }^{\prime }$, $\kappa$, and $\lambda$ phases of $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}X$ [bis(ethylenedithio)tetrathiafulvalene] and $(\mathrm{B}\mathrm{E}\mathrm{T}\mathrm{S}{)}_{2}X$ [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a $d_{x^2-y^2}$ superconductor with a small superfluid stiffness and a pseudogap with $d_{x^2-y^2}$ symmetry.