Charge-order on the triangular lattice: Effects of next-nearest-neighbor attraction in finite temperatures.

The extended Hubbard model in the atomic limit, which is equivalent to lattice S = 1 / 2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W 1) and next-nearest-neighbor (W 2) density–density intersite interactions. The variational approach treating the U term exactly and the W l terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T > 0) phase diagrams (as a function of particle concentration) for W 1 > 0 and W 2 < 0. Two different types of charge-order (i.e., DCO and TCO phases) within 3 × 3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W 2 < 0 stabilizes PS states at T = 0 and it extends the regions of their occurrence at T > 0. The evolution of the diagrams with increasing of | W 2 | / W 1 is investigated. It is found that some of the PS states are stable only at T > 0. Two different critical values of | W 2 | / W 1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist. • Atomic limit of the extended Hubbard model on the triangular lattice is analyzed. • Phase diagrams of the lattice S = 1 / 2 fermionic gas model are found. • The effects of next-nearest-neighbor attractive interaction are investigated. • The diagrams have complex structure with different multicritical points. • The stability regions of various phase separated states are found. [ABSTRACT FROM AUTHOR]