Spinless charges on the triangular lattices in the strong repulsion limit: possibility of a new charge ordered liquid

We propose a new type of charge ordered liquid state in the spinless fermion system on a triangular lattice under strong inter-site Coulomb interactions, $V$. In the absence of fermion hoppings, the ground state is disordered due to geometrical frustration. Introduction of hopping terms lifts the degeneracy and drives the system to a metalic state with possible partial charge orders, which we call a ``pinball liquid''. There, a gapless charge liquid component moves around a possible long range ordered Wigner crystal solid component. This liquid state is dominant over wide range of filling, $n=1/3 \sim 2/3$. When an anisotropy in $V$ exceeds its critical value at half-filling $n=1/2$, an metal-insulator transition accompanied by another charge order with a different periodicity is induced. Relevance to the organic conductors $\theta$-ET$_2$X which show novel nonlinear transport properties is discussed.\\ REFERENCES:\\ \qquad cond-mat/0605045, cond-mat/0607181, cond-mat/0607717.