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 on-site 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 us 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 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 further research with correlation effects included. Together with the atomic-limit approximation it can serve as both a starting point and a tool to interpret results.

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• Charge order
• Phase transitions
• Quantum phase transitions
• Lattice models in statistical physics
• Triangular lattice
• Two-dimensional electron gas
• Two-dimensional electron system
• Extended Hubbard model
• Lattice models in condensed matter
• Mean field theory
• Mean-field & cluster methods