Quantitative mappings between symmetry and topology in solids

Nature Communications
Zhida SongChen Fang

Abstract

The study of spatial symmetries was accomplished during the last century and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard first-principles calculation. On the other hand, the topological data (topological invariants), the defining quantities of nontrivial topological states, are in general considerably difficult to obtain, and this difficulty has critically slowed down the search for topological materials. Here we provide explicit and exhaustive mappings from symmetry data to topological data for arbitrary gapped band structure in the presence of time-reversal symmetry and any one of the 230 space groups. The mappings are completed using the theoretical tools of layer construction and symmetry-based indicators. With these results, finding topological invariants in any given gapped band structure reduces to a simple search in the mapping tables provided.

References

Nov 1, 1993·Physical Review. B, Condensed Matter·G Kresse, J Hafner
Aug 17, 1987·Physical Review Letters·I AffleckH Tasaki
Oct 26, 2005·Physical Review Letters·C L Kane, E J Mele
Dec 16, 2006·Science·B Andrei BernevigShou-Cheng Zhang
Mar 16, 2007·Physical Review Letters·Liang FuE J Mele
Sep 22, 2007·Science·Markus KönigShou-Cheng Zhang
Apr 8, 2011·Physical Review Letters·Liang Fu
Aug 7, 2012·Nature Communications·Timothy H HsiehLiang Fu
Oct 2, 2012·Nature Materials·P DziawaT Story
Apr 15, 2016·Nature·Zhijun WangB Andrei Bernevig
Jul 2, 2017·Nature Communications·Hoi Chun PoHaruki Watanabe
Jul 21, 2017·Nature·Barry BradlynB Andrei Bernevig
Dec 30, 2017·Physical Review Letters·Zhida SongChen Fang

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Citations

Jan 4, 2020·Science Advances·Zhida SongMichael Hermele
Feb 28, 2020·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Hoi Chun Po
Jul 16, 2020·Advanced Materials·Yanjun MaChang-Beom Eom
Mar 1, 2019·Nature·M G VergnioryZhijun Wang
Feb 2, 2020·Nature Communications·Benjamin J WiederB Andrei Bernevig
Mar 16, 2019·Science Advances·Feng TangXiangang Wan
Jan 11, 2020·Physical Review Letters·T T ZhangM P M Dean
Mar 1, 2019·Nature·Tiantian ZhangChen Fang
Feb 29, 2020·Physical Review Letters·Chengwang NiuYing Dai
May 20, 2020·Science Advances·Seishiro OnoHaruki Watanabe
Jun 15, 2019·Proceedings of the National Academy of Sciences of the United States of America·Chuang-Han HsuLiang Fu
Feb 15, 2020·Science·Valerio PeriSebastian D Huber
Oct 23, 2020·Physical Chemistry Chemical Physics : PCCP·Asadollah BafekryBohayra Mortazavi
Nov 20, 2020·Proceedings of the National Academy of Sciences of the United States of America·Quentin MarsalAdolfo G Grushin
Mar 27, 2021·Nature Communications·Kyungchan LeeAdam Kaminski
Jul 17, 2021·Physical Review Letters·Zhi-Da SongAdy Stern
Oct 15, 2021·Nature Communications·Luis ElcoroB Andrei Bernevig

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