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Hyperbolic band topology with non-trivial second Chern numbers
Weixuan Zhang1,2, Fengxiao Di1,2, Xingen Zheng1,2
1Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, 100081, Beijing, China.
Nature Communications
|February 25, 2023
Summary
Researchers engineered hyperbolic topological band insulators with a non-trivial second Chern number, not protected by the first Chern number. This work introduces novel hyperbolic topological states with higher-order invariants.
Area of Science:
- Condensed Matter Physics
- Non-Euclidean Geometry
- Topological Materials
Background:
- Topological band theory provides a framework for classifying topological matter.
- Hyperbolic lattices in non-Euclidean space can be analyzed using hyperbolic Bloch theorem.
- Previous work proposed hyperbolic topological band insulators protected by first Chern numbers.
Purpose of the Study:
- To construct hyperbolic topological band insulators with a vanished first Chern number but a non-trivial second Chern number.
- To explore higher-order topological invariants in hyperbolic systems.
- To experimentally detect these novel hyperbolic topological states.
Main Methods:
- Developing a model with non-abelian translational symmetry of {8,8} hyperbolic tiling.
- Engineering intercell couplings and onsite potentials within unit cells.
- Fabricating finite hyperbolic circuit networks with varied boundary conditions for experimental detection.
Main Results:
- Successfully constructed hyperbolic topological band insulators featuring quantized second Chern numbers.
- Demonstrated the appearance of non-trivial bandgaps through engineered couplings and potentials.
- Experimental detection of these hyperbolic topological states was achieved.
Conclusions:
- This study presents a new method for engineering hyperbolic topological band insulators.
- The findings highlight the possibility of realizing topological states with higher-order invariants.
- The research expands the understanding of topological band theory in non-Euclidean geometries.
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