Particle-Hole Asymmetry and Pinball Liquid in a Triangular-Lattice Extended Hubbard Model within Mean-Field Approximation

Abstract

Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly-correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive onsite and nearest-neighbor interaction, arbitrary charge concentration, and $\sqrt{3}\times\sqrt{3}$ supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify $8$ charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.

Figures (9)

• Figure 1: The non-interacting band structures (left) and densities of states (right) of (a) triangular, (b) triangular with the $\sqrt{3}\times\sqrt{3}$ supercell, and (c) honeycomb lattices.
• Figure 2: The MFA phase diagram of the triangular-lattice EHM with 3-sublattices as a function of $V$ and $\bar{\mu} = \mu - U/2 - zV$ for $U=0D$ and $U=2D$. Only the phases with the smallest grand potential are shown. The subscripts in the phase names refer to the charge order (see Fig. \ref{['fig:structures']}) while letters M and I stand for the metallic and insulating phase, respectively. The solid and dashed lines represent continuous and discontinuous phase transitions, respectively. The dotted line is placed at the approximate transition where the charge-ordered metal is not a pinball liquid (PL) anymore. The total concentration is constant along the green dashed lines, in particular $n=$ 1/3, 2/3, 1, 4/3, and 5/3 (from left to right).
• Figure 3: The found charge order types on the triangular lattice. The color of the circles represent the relative charge concentration on the lattice sites: from the highest (black circles) to the lowest (white circles). The $\sqrt{3}\times\sqrt{3}$ supercell is shown by the dashed lines. The figure is prepared using VESTA program Vesta.
• Figure 4: The order parameters in the $AAB$ region (left) and representative band structures of the $AAB$ phases (right). The vertical dashed lines show the locations of phase transitions.
• Figure 5: Comparison between the lower bands of an $AAB$-region phase (solid lines) and the non-interacting honeycomb bands (shifted to $\omega_A$).