Hierarchical ground-state crystals underlying Hertzian quasicrystals.

Yao Li, Yiwei Wang, Yingke Geng, Wenyu Liu, Fangfu Ye, Jeff Z Y Chen

Abstract read

In one paragraph

Article in Nature communications, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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0citing papers in PubMed

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1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

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Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

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0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

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5 · Who and what money

Authors and funding

6 authors.

Yao LiSchool of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, China. liyao@nankai.edu.cn.ORCID http://orcid.org/0000-0002-7926-7597

Yiwei WangSchool of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, China.

Yingke GengSchool of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, China.

Wenyu LiuSchool of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, China.

Fangfu YeBeijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China. fye@iphy.ac.cn.

Jeff Z Y ChenDepartment of Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada. jeffchen@uwaterloo.ca.ORCID http://orcid.org/0000-0002-7994-6231

Funding

National Natural Science Foundation of China (National Science Foundation of China) 12275137

6 · The paper itself

Abstract

As a simple physics model for crystal and quasicrystal formation, the Hertzian potential describes the interaction between two soft-core colloidal particles. However, explaining why quasicrystals emerge in such a minimal model remains a theoretical challenge. Here, using analytically exact approaches, we reveal multiple layers of hierarchical crystal patterns that serve as the energy ground states underlying quasicrystals found by computer simulations. Our findings offer a new perspective on quasicrystal formation.

Identifiers

PMID41290679

DOI10.1038/s41467-025-66158-0

PMCPMC12717090

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