λ-Jellium Model for the Anomalous Hall Crystal

Area of Science:

• Condensed Matter Physics
• Quantum Geometry
• Topological Matter

Background:

• The standard jellium model exhibits metallic and Wigner crystal phases.
• Its vanishing Berry curvature limits studies of systems with strong interactions and quantum geometry.
• The anomalous Hall crystal (AHC) is a topological Wigner crystal variant with nonzero Chern number.

Purpose of the Study:

• Introduce λ-jellium, a tunable extension of the jellium model.
• Systematically explore Berry curvature's effect on electron crystallization.
• Investigate the phase diagram of interacting electrons with nontrivial quantum geometry.

Main Methods:

• Self-consistent Hartree-Fock calculations.
• Phase diagram analysis of the λ-jellium model.
• Exploration of electron crystallization driven by Berry curvature.

Main Results:

• The AHC phase is extensive in the phase diagram.
• Identified two distinct Wigner crystal phases and two Fermi liquid phases.
• Observed a continuous phase transition between AHC and a Wigner crystal phase.
• Discovered nontriangular lattice geometries in parts of the AHC phase.

Conclusions:

• The λ-jellium model provides a tunable platform for studying electron systems with Berry curvature.
• Quantum geometry significantly influences electron crystallization and phase transitions.
• The model serves as a foundation for advanced numerical studies in topological condensed matter.