Topological Quantum Transition Driven by Charge-Phonon Coupling in the Haldane Chern Insulator

Area of Science:

• Condensed matter physics
• Topological quantum phenomena

Background:

• Topological properties are crucial for understanding condensed matter systems.
• The Haldane model on a honeycomb lattice is a key example of a Chern insulator.

Purpose of the Study:

• To investigate the impact of charge-phonon coupling on the topological properties of the spinless Haldane model.
• To identify indicators of a topological quantum transition driven by electron-lattice interactions.

Main Methods:

• Theoretical analysis of the spinless Haldane model.
• Numerical simulations to study system behavior under varying charge-phonon coupling strengths.
• Analysis of fermion occupation at the Dirac point and phonon propagator characteristics.

Main Results:

• Increasing charge-phonon coupling drives the system from a topological Chern insulator phase to a trivial insulator phase.
• A finite discontinuity in the average number of fermions at the Dirac point signals the topological quantum transition.
• The phonon propagator shows a two-peak structure near the transition, with potential charge density wave instability.

Conclusions:

• Charge-phonon coupling can fundamentally alter the topological state of matter.
• The fermion occupation at the Dirac point serves as a direct experimental probe for topological transitions.
• Electron-lattice interactions are critical in determining the insulating properties and potential instabilities in topological materials.