Failure of RVB theory to give superconductivity in layered quasi-two dimensional organic charge transfer solids

The discovery of high Tc superconductivity in doped cuprates and the consequent proposal of Anderson's RVB theory have brought much focus on the Mott insulators as a novel phase. Following this, RVB mean field and other related theories developed in 1/2-filled band systems have also been applied to study the pressure-induced Mott insulator-to-superconductor transition (without external doping) in the layered quasi-two-dimensional organic charge transfer solids (CTS) like $\kappa$-(BEDT-TTF)$_2$X. We show that although the antiferromagnetic phase of these highly dimerized CTS can be described within effective half-filled band Hubbard or Hubbard-Heisenberg models, the superconducting phase is absent within these models. The so-called valence bond solid that has been found in EtMe$_{3}$P[Pd(dmit)$_{2}$]$_{2}$ is also absent within the effective 1/2-filled band model. We conclude that the effective 1/2-filled band models give an incomplete description of the layered CTS and are thus inappropriate for such systems.