Metal-insulator transition in the quarter-filled frustrated checkerboard lattice

We study the electronic structure and correlations in the geometrically frustrated two dimensional checkerboard lattice. In the large U limit considered here we start from an extended Hubbard model of spinless fermions at half-filling. We investigate the model within two distinct Green's function approaches: In the first approach a single-site representation decoupling scheme is used that includes the effect of nearest neighbor charge fluctuations. In the second approach a cluster representation leading to a 'multiorbital' model is investigated which includes intra-cluster correlations more rigorously and those between clusters on a mean field basis. It is demonstrated that with increasing nearest-neighbor Coulomb interaction V both approaches lead to a metal-insulator transition with an associated 'Mott-Hubbard' like gap caused by V. Within the single site approach we also explore the possibility of charge order. Furthermore we investigate the evolution of the quasiparticle bands as funtion of V.