We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the and Љ crystal structures. DOI: 10.1103/PhysRevB.66.195102 PACS number͑s͒: 71.27.ϩa, 71.30.ϩh Charge ordering in strongly correlated electron systems is currently under intense investigation. Charge ordering is relevant to a broad range of materials including cuprates, 1 manganates, 2 magnetite, 3 vanadium oxides, 4 and Bechgaard salts. 5 and Љ types of layered molecular crystals based on molecules such as BEDT-TTF ͑bisethylenedithio-tetrathiafulvalene͒ ͑Ref. 6͒, display charge ordering, metallic, and superconducting phases close to each other. 7 Charge ordering driven by a strong intersite Coulomb repulsion 8,9 is possible in crystals with and Љ arrangements of BEDT-TTF molecules because their bands are quarter-filled with holes, in contrast to the well-studied -type, crystals for which strong dimerization of the molecules lead to a halffilled band. 10 -type crystals undergo a transition from a metal to a charge-ordered insulator as the temperature, pressure, uniaxial stress, or anion is varied. 7,8 Furthermore, the metallic phase exhibits features characteristic of a strongly correlated system. In particular, the optical conductivity spectra display a broad midinfrared band and the near absence of a Drude-like peak. 11 This is in contrast to conventional metals, for which the total spectral weight is dominated by a Drude peak.In this paper, we use the results of an exact diagonalization study of the relevant extended Hubbard model to argue that the intersite Coulomb repulsion is responsible for the observed metal-insulator transition in the and Љ crystals. We show how the Drude weight decreases as the intersite Coulomb repulsion V is increased, until, at a finite value of V, a transition to an insulating phase occurs. Simultaneously, long-range charge ordering gradually sets in. We further find that a redistribution of the optical conductivity spectra occurs close to the metal-insulator transition. This finding is in qualitative agreement with experimental data on and Љ organic salts. 11-14 Our results are relevant to the optical response of sodium vanadates, such as -Na 0.33 V 2 O 3 , which also display charge ordering.The quarter-filled extended Hubbard model on a square lattice is the simplest strongly correlated model that can potentially describe the competition between metallic, superconducting, and insulating phases in the and Љ materials. 15,16 The Hamiltonian is
͑1͒where c i † creates an electron of spin at site i. For Vϭ0, previous calculations suggested that the system is metallic with no charge order. 17 In the limit of U,Vӷt the double o...