Strong coupling theory of the spinless charges on triangular lattices: Possible formation of a gapless charge-ordered liquid

We propose an existence of charge-ordered liquid state in the spinless fermion system on a triangular lattice under strong intersite Coulomb interactions, V. The classical ground state in the strong coupling limit is disordered due to geometrical frustration. The introduction of a quantum hopping term lifts the degeneracy and drives the system to a partially ordered phase, which we call a pinball liquid. A possibly long-range-ordered Wigner-crystal solid coexists with a liquid component which is moving around them like a pinball. This liquid is dominant over a wide range of filling and even away from the regular triangle. Relevance to the organic theta-ET2X is discussed.