Competition between Charge Ordering and Superconductivity in Layered Organic Conductors $\alpha$-(BEDT-TTF)$_2M$Hg(SCN)$_4$ (M = K, NH$_4$)

While the optical properties of the superconducting salt $\alpha$-(BEDT-TTF)$_2$NH$_4$Hg(SCN)$_4$ remain metallic down to 2 K, in the non-superconducting K-analog a pseudogap develops at frequencies of about 200 cm$^{-1}$ for temperatures T < 200 K. Based on exact diagonalisation calculations on an extended Hubbard model at quarter-filling we argue that fluctuations associated with short range charge ordering are responsible for the observed low-frequency feature. The different ground states, including superconductivity, are a consequence of the proximity of these compounds to a quantum phase charge-ordering transition driven by the intermolecular Coulomb repulsion.