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C-symmetric Chern insulators.

Ying Han¹, Ai-Lei He²

¹State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|March 15, 2021

Summary

This study introduces methods to identify and analyze topological phase transitions in curved Chern insulators (CIs) on novel lattice geometries. Researchers explore CIs with n-fold rotational symmetry, advancing quantum Hall state research.

Keywords:

Chern insulators n-fold rotational symmetry quantum transports real-space Chern number

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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.