Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect

Department of Materials Science and Optoelectronic Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan Institute of Materials Science and Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan, R.O.C. Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom Division of Information and Communication Sciences, Macquarie University, NSW 2109, Australia Department of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon 440-746, Korea National Measurement Laboratory, Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu 300, Taiwan Department of Physics, National Taiwan University, Taipei 106, Taiwan, R.O.C.