C-symmetric Chern insulators

Area of Science:

• Condensed Matter Physics
• Topological Materials Science
• Quantum Phenomena

Background:

• Chern insulators (CIs) are crucial for realizing quantum Hall states without magnetic fields.
• Existing research on CIs has explored various curved lattices, including cone-like structures and fullerenes.
• Identifying curved CIs and understanding their topological phase transitions (TPTs) remain underexplored areas.

Purpose of the Study:

• To systematically investigate curved CIs with arbitrary n-fold rotational symmetry (C_n-symmetric CIs).
• To explore topological phase transitions in these curved CIs.
• To establish robust methods for identifying and characterizing curved CIs.

Main Methods:

• Utilized a 'cutting and gluing' approach with disk geometry to construct C_n-symmetric CIs on cone-like and saddle-like lattices.
• Proposed and applied two methods for calculating the real-space Chern number: Kitaev's formula and the local Chern marker.
• Investigated TPTs by tuning parameters such as staggered flux and on-site mass.

Main Results:

• Successfully identified C_n-symmetric CIs on curved lattices.
• Demonstrated that chiral edge states, real-space Chern number, and quantized conductance are key identifiers for these curved CIs.
• Characterized TPTs in curved CIs through parameter manipulation.

Conclusions:

• The study provides a comprehensive framework for identifying and analyzing curved Chern insulators and their topological phase transitions.
• The proposed methods offer new tools for exploring topological properties in curved material systems.
• This work advances the understanding of topological states in non-Euclidean geometries.