Electronic ferroelectricity in the falicov-kimball model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics

Background:

• The Falicov-Kimball model is a key theoretical framework for understanding electron correlations in materials.
• Investigating strong coupling limits is crucial for uncovering novel electronic phases.

Purpose of the Study:

• To demonstrate the existence of spontaneous electric polarization in the Falicov-Kimball model.
• To determine the phase diagram of the strongly interacting Falicov-Kimball model.

Main Methods:

• Mapping the strong coupling limit of the Falicov-Kimball model to an XXZ spin 1/2 model with a magnetic field.
• Analysis of the resulting spin model to identify distinct phases.

Main Results:

• Existence of spontaneous electric polarization in the model solution.
• Identification of a phase transition to a mixed-valence regime.
• Characterization of two distinct phases within the mixed-valence regime: an orbitally ordered state and Bose-Einstein condensation of excitons.

Conclusions:

• The Falicov-Kimball model exhibits spontaneous electric polarization under strong coupling.
• The transition to a mixed-valence regime reveals complex electronic behavior, including excitonic condensation with inherent polarization.