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

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• Adsorbed atoms often form triangular lattices on crystal surfaces.
• Lattice gas models are used to study particle arrangements and interactions.
• The extended Hubbard model describes interacting particles on a lattice.

Purpose of the Study:

• To extend the lattice gas model to S=1/2 fermionic particles on a 2D triangular lattice.
• To analyze the phase diagrams and thermodynamic properties of this extended model.
• To investigate the effects of onsite (U) and intersite (W1, W2) interactions.

Main Methods:

• Variational approach treating onsite interaction exactly.
• Mean-field approximation for intersite interactions.
• Analysis of ground state (T=0) and finite temperature (T>0) phase diagrams.

Main Results:

• Two types of charge order within a 3x3 unit cell can occur.
• Phase separation is stabilized by attractive W2 interactions at incommensurate fillings.
• Specific interaction ratios (U/W1) lead to distinct ordered phases and phase-separated states.

Conclusions:

• The model exhibits complex phase behavior dependent on interaction parameters and temperature.
• Phase separation and charge ordering are key features of this fermionic lattice gas model.
• Qualitative differences exist compared to models on hypercubic lattices.