Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to [Formula: see text] fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite [Formula: see text] and [Formula: see text] (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive [Formula: see text] , the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state ([Formula: see text]) diagram for [Formula: see text] as well as finite temperature ([Formula: see text]) phase diagrams for [Formula: see text] are presented. Two different types of charge order within [Formula: see text] unit cell can occur. At [Formula: see text] , for [Formula: see text] phase separated states are degenerated with homogeneous phases (but [Formula: see text] removes this degeneration), whereas attractive [Formula: see text] stabilizes phase separation at incommensurate fillings. For [Formula: see text] and [Formula: see text] only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive [Formula: see text] the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.