Critical Dimerization Strength of the Quarter-Filled t-J Model

An exact-diagonalization technique on small clusters is used to study the ground state of the dimerized t-J model at quarter filling. The equal-time charge and spin correlations, charge and spin gaps, and binding energy are calculated for the two-dimensional lattice with a spatial dimerization pattern corresponding to organic conductors $\kappa-(BEDT-TTF)_2X$. We show that competition between the effects of two types of dimerization, i.e., dimerization in the hopping integral and dimerization in the exchange interaction, leads to the insulator-superconductor transition in the ground state of the model. The phase diagram is thereby presented.