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.