Route towards Localization for Quantum Anomalous Hall Systems with Chern Number 2

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Phenomena

Background:

• The quantum anomalous Hall effect (QAHE) is a topological phenomenon observed in certain magnetic materials.
• Disorder can significantly impact topological phases, potentially leading to localization.
• Previous studies suggested a direct transition from Chern number 2 to Chern number 0 in disordered systems.

Purpose of the Study:

• To investigate the topological origin of the direct transition from Chern number 2 to Chern number 0 in disordered quantum anomalous Hall systems.
• To identify and characterize any intermediate topological states during this localization process.
• To understand the universality of this phenomenon in high Chern number insulators.

Main Methods:

• Calculation of band structures for disordered supercells.
• Determination of Chern numbers for various system configurations.
• Numerical scaling of conductances to analyze renormalization group flows.
• Investigation of model modifications to stabilize intermediate states.

Main Results:

• A hidden Chern number 1 state was identified on the route to localization.
• This intermediate state is too short-lived and fluctuating to be directly observed.
• The Chern number 1 state acts as an unstable fixed point in the renormalization group flow.
• Attempts to stabilize this intermediate state through model design were unsuccessful.

Conclusions:

• The direct transition from Chern number 2 to Chern number 0 in disordered QAHE systems is attributed to an unobservable, unstable Chern number 1 intermediate state.
• This phenomenon is likely universal for insulators with high Chern numbers.
• The findings offer a distinct perspective on topological phase transitions and can guide future experimental and theoretical research.