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Quantitative mappings between symmetry and topology in solids
Zhida Song1,2, Tiantian Zhang1,2, Zhong Fang1
1Beijing National Research Center for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
Nature Communications
|September 1, 2018
Summary
Discovering topological materials is simplified. This study maps crystal symmetry data to topological data, making it easier to find topological invariants in solids.
Area of Science:
- Condensed matter physics
- Solid-state physics
- Crystallography
Background:
- Spatial symmetries are well-understood and readily extracted from first-principles calculations for crystalline solids.
- Topological data, crucial for identifying nontrivial topological states, are generally difficult to obtain.
- This difficulty has hindered the discovery of new topological materials.
Purpose of the Study:
- To establish explicit and exhaustive mappings between symmetry data and topological data.
- To cover arbitrary gapped band structures with time-reversal symmetry and any of the 230 space groups.
- To simplify the process of finding topological invariants.
Main Methods:
- Utilizing the theoretical framework of layer construction.
- Employing symmetry-based indicator theory.
- Developing comprehensive mapping tables.
Main Results:
- Provided explicit and exhaustive mappings from symmetry data to topological data.
- Established a direct link between crystal symmetries and topological invariants.
- Created a searchable resource for topological data extraction.
Conclusions:
- The search for topological materials is significantly accelerated.
- Identifying topological invariants is reduced to a simple lookup in the provided mapping tables.
- This work provides a powerful tool for materials science and condensed matter physics research.
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