Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Hofstadter's butterfly is a fractal pattern arising from competing lattice periodicity and magnetic fields.
• Predicting topological invariants for disordered materials or those lacking a spectral gap is currently challenging.
• Existing methods struggle with complex material systems, limiting fundamental inquiries and material discovery.

Purpose of the Study:

• To develop a novel framework for predicting local Chern markers using a position-space description.
• To validate this framework against experimental quantum transport data in artificial graphene.
• To explore the emergence of Hofstadter's butterfly and identify topological phase transitions in material systems.

Main Methods:

• Utilizing a position-space description to calculate local Chern markers.
• Experimentally observing quantum transport in artificial graphene heterostructures.
• Simulating the emergence of Hofstadter's butterfly from an unpatterned 2D electron gas.

Main Results:

• The framework successfully predicts local Chern markers, accounting for disorder that closes the bulk spectral gap.
• Topological origins of antidot-localized states in artificial graphene under magnetic fields were revealed.
• The simulation showed Hofstadter's butterfly formation and predicted a topological insulator phase transition.

Conclusions:

• A position-space approach enables Chern invariant determination without prior knowledge of occupied states or bulk spectral gaps.
• This method facilitates fundamental research in metallic, aperiodic, and disordered systems.
• The framework offers a novel route for material discovery and understanding complex topological phenomena.