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

Abstract

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 $\sqrt{3}\times \sqrt{3}$ 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.

arXiv comment7 pages, 5 figures, 57 references; pdf-RevTeX class used. This is the author created version of an article accepted for publication in J. Magn. Magn. Matter (Elsevier) journal. The article has been published on a gold open access basis under a CC BY 4.0 licence

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