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We present an resonating valence bond (RVB) theory of superconductivity forthe Hubbard--Heisenberg model on an anisotropic triangular lattice. We showthat these calculations are consistent with the observed phase diagram of thehalf-filled layered organic superconductors, such as the beta, beta', kappa andlambda phases of (BEDT-TTF)_2X [bis(ethylenedithio)tetrathiafulvalene] and(BETS)_2X [bis(ethylenedithio)tetraselenafulvalene]. We find a first ordertransition from a Mott insulator to a d_{x^2-y^2} superconductor with a smallsuperfluid stiffness and a pseudogap with d_{x^2-y^2} symmetry. TheMott--Hubbard transition can be driven either by increasing the on-site Coulombrepulsion, U, or by changing the anisotropy of the two hopping integrals, t'/t.Our results suggest that the ratio t'/t plays an important role in determiningthe phase diagram of the organic superconductors.Comment: 4 pages, 3 figur

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