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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Porous Haldane model: topological phase transitions and flat bands
Fan Yang1, Yi-Xuan Ling1, Xu-Hui Yan1
1College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, People's Republic of China.
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|November 25, 2024
Summary
We introduce a porous Haldane model to study nanoholes in Chern insulators (CIs). This model reveals novel topological phases, including higher-order topological insulators with unique edge and corner states.
Area of Science:
- Condensed Matter Physics
- Topological Materials
- Quantum Matter
Background:
- Chern insulators (CIs) are topological states of matter with unique electronic properties.
- Understanding the impact of structural modifications like nanoholes is crucial for novel material design.
- Higher-order topological insulators (HOTIs) exhibit protected states at boundaries of lower dimensionality.
Purpose of the Study:
- To investigate the influence of nanoholes on Chern insulators (CIs).
- To propose and analyze a porous Haldane model incorporating nearest-neighbor (NN) and next-nearest-neighbor (NNN) hoppings with staggered magnetic fluxes.
- To explore the emergence of various topological phases, including HOTIs, and their unique properties.
Main Methods:
- Development of a porous Haldane model with NN and NNN hoppings and staggered magnetic fluxes.
- Analysis of topological phase diagrams at different filling factors (2/5, 9/20, and half-filling).
- Characterization of edge and corner states, including quantized quadrupole moments and topological flat bands (TFBs).
Main Results:
- Multiple Chern insulator (CI) phases with varying Chern numbers (C=±1, ±2, ±3, ±4) were identified at 2/5 filling.
- CI phases (C=±1, ±2, ±3) and HOTI phases were observed at 9/20 filling.
- At half-filling, CI phases (C=±1, ±2, -3) and HOTI phases emerged. The HOTI phases exhibit gapless edge states and robust corner states with quantized quadrupole moments.
- A topological flat band (TFB) with a flatness ratio of approximately 13 was found.
- A fractional CI state (ν=1/2) with hard-core bosons was investigated using the TFB model.
Conclusions:
- The porous Haldane model effectively captures the influence of nanoholes on CIs, leading to diverse topological phases.
- The discovered HOTI phases possess unique characteristics, including gapless edge states and quantized corner states.
- The presence of a TFB opens avenues for exploring fractional topological states, such as the ν=1/2 fractional CI state with hard-core bosons.
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