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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 |
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 |
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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.
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Received: 18 July 2013
Revised: 11 September 2013
Accepted manuscript online:
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PACS:
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73.43.Nq
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(Quantum phase transitions)
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71.23.An
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(Theories and models; localized states)
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72.80.Vp
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(Electronic transport in graphene)
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| Fund: 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). |
Corresponding Authors:
Sheng Li, Xing Ding-Yu
E-mail: shengli@nju.edu.cn;dyxing@nju.edu.cn
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Cite this article:
Zhang Yi-Fu (张议夫), Yang Yun-You (杨运友), Ju Yan (鞠艳), Sheng Li (盛利), Shen Rui (沈瑞), Sheng Dong-Ning (盛冬宁), Xing Ding-Yu (邢定钰) Coupling-matrix approach to the Chern number calculation in disordered systems 2013 Chin. Phys. B 22 117312
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