中国物理B ›› 2013, Vol. 22 ›› Issue (11): 117312-117312.doi: 10.1088/1674-1056/22/11/117312

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Coupling-matrix approach to the Chern number calculation in disordered systems

张议夫a, 杨运友b, 鞠艳a, 盛利a, 沈瑞a, 盛冬宁c, 邢定钰a   

  1. a National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China;
    b College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, China;
    c Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
  • 收稿日期:2013-07-18 修回日期:2013-09-11 出版日期:2013-09-28 发布日期:2013-09-28
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant Nos. 2009CB929504, 2011CB922103, and 2010CB923400), the National Natural Science Foundation of China (Grant Nos. 11225420, 11074110, 11174125, 11074109, 11074111, and 91021003), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010364), the US NSF (Grant Nos. DMR-0906816 and DMR-1205734), and the Princeton MRSEC (Grant No. DMR-0819860).

Coupling-matrix approach to the Chern number calculation in disordered systems

Zhang Yi-Fu (张议夫)a, Yang Yun-You (杨运友)b, Ju Yan (鞠艳)a, Sheng Li (盛利)a, Shen Rui (沈瑞)a, Sheng Dong-Ning (盛冬宁)c, Xing Ding-Yu (邢定钰)a   

  1. a National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China;
    b College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, China;
    c Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
  • Received:2013-07-18 Revised:2013-09-11 Online:2013-09-28 Published:2013-09-28
  • Contact: Sheng Li, Xing Ding-Yu E-mail:shengli@nju.edu.cn;dyxing@nju.edu.cn
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant Nos. 2009CB929504, 2011CB922103, and 2010CB923400), the National Natural Science Foundation of China (Grant Nos. 11225420, 11074110, 11174125, 11074109, 11074111, and 91021003), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010364), the US NSF (Grant Nos. DMR-0906816 and DMR-1205734), and the Princeton MRSEC (Grant No. DMR-0819860).

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摘要： The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.

关键词: Chern number, topology, disorder

Abstract: The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.

Key words: Chern number, topology, disorder

中图分类号:  (Quantum phase transitions)

  • 73.43.Nq
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