An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model

doi:10.1088/1674-1056/ae69bf

中国物理B ›› 2026, Vol. 35 ›› Issue (7): 76102-076102.doi: 10.1088/1674-1056/ae69bf

An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model

Tian-Ze Li(李天择)¹, Chang-Chun He(何长春)^1,2, and Xiao-Bao Yang(杨小宝)^1,†

1 School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China;
2 Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China

收稿日期:2026-02-15 修回日期:2026-05-05 接受日期:2026-05-07 发布日期:2026-07-10
通讯作者: Xiao-Bao Yang E-mail:scxbyang@scut.edu.cn
基金资助:
This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 12474228 and 12504268) and the Fund of State Key Laboratory of Quantum Functional Materials (Grant No. QFM2025KF008).

An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model

Tian-Ze Li(李天择)¹, Chang-Chun He(何长春)^1,2, and Xiao-Bao Yang(杨小宝)^1,†

1 School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China;
2 Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China

Received:2026-02-15 Revised:2026-05-05 Accepted:2026-05-07 Published:2026-07-10
Contact: Xiao-Bao Yang E-mail:scxbyang@scut.edu.cn
Supported by:
This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 12474228 and 12504268) and the Fund of State Key Laboratory of Quantum Functional Materials (Grant No. QFM2025KF008).

1. 2026-076102-SI.pdf(4016KB)

摘要/Abstract

摘要： The special quasirandom structure (SQS) method provides an ideal representation of disordered structures. However, it is still a challenge to generate structures that perfectly satisfy the constraints of correlation functions, especially for many-body interactions. Taking one-dimensional systems as an example, we develop an efficient SQS construction algorithm for multi-component materials based on De Bruijn sequences, which can be extended to systems with higher dimensions and more components. The SQSs constructed by our algorithm are shown to universally satisfy all the constraints of 1 ~ n-body interactions, and the numbers of consecutive identical-atom subsequences follow a unified counting rule. Based on the Kronig–Penney model, we have systematically investigated the impact of structural disorder on electronic properties. As the cell size increases, there are the same trends in the electronic structures obtained from SQSs and fully random structures, while SQSs display markedly faster convergence and significantly reduced fluctuations. We demonstrate that SQS provides a reliable and efficient finite-size representation for electronic-structure calculations of disordered systems.

关键词: disordered structure, special quasirandom structure, De Bruijn sequence, Kronig-Penney model

Abstract: The special quasirandom structure (SQS) method provides an ideal representation of disordered structures. However, it is still a challenge to generate structures that perfectly satisfy the constraints of correlation functions, especially for many-body interactions. Taking one-dimensional systems as an example, we develop an efficient SQS construction algorithm for multi-component materials based on De Bruijn sequences, which can be extended to systems with higher dimensions and more components. The SQSs constructed by our algorithm are shown to universally satisfy all the constraints of 1 ~ n-body interactions, and the numbers of consecutive identical-atom subsequences follow a unified counting rule. Based on the Kronig–Penney model, we have systematically investigated the impact of structural disorder on electronic properties. As the cell size increases, there are the same trends in the electronic structures obtained from SQSs and fully random structures, while SQSs display markedly faster convergence and significantly reduced fluctuations. We demonstrate that SQS provides a reliable and efficient finite-size representation for electronic-structure calculations of disordered systems.

Key words: disordered structure, special quasirandom structure, De Bruijn sequence, Kronig-Penney model

中图分类号: (Amorphous semiconductors, metals, and alloys)

61.43.Dq

71.23.-k (Electronic structure of disordered solids) 02.70.-c (Computational techniques; simulations)

Tian-Ze Li(李天择), Chang-Chun He(何长春), and Xiao-Bao Yang(杨小宝). An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model[J]. 中国物理B, 2026, 35(7): 76102-076102.

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An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model

An efficient algorithm for generating perfect special quasirandom structures with many-body correlation functions and its application to the Kronig-Penney model

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