About the Authors

Kai Gong

Affiliations Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, People's Republic of China, Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China

Ming Tang

tangminghuang521@hotmail.com (MT); pmhui@phy.cuhk.edu.hk (PMH)

Affiliations Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, People's Republic of China, Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China, Department of Mathematics, Kyungpook National University, Daegu, South Korea

Pak Ming Hui

tangminghuang521@hotmail.com (MT); pmhui@phy.cuhk.edu.hk (PMH)

Affiliation Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China

Hai Feng Zhang

Affiliation School of Mathematical Science, Anhui University, Hefei, People's Republic of China

Do Younghae

Affiliation Department of Mathematics, Kyungpook National University, Daegu, South Korea

Ying-Cheng Lai

Affiliations Department of Mathematics, Kyungpook National University, Daegu, South Korea, School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona, United States of Ameica

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: MT PMH YCL YD. Performed the experiments: KG MT HFZ. Analyzed the data: KG MT PMH YCL. Contributed reagents/materials/analysis tools: KG PMH YD. Wrote the paper: KG MT PMH YD YCL.