Critical Exponent for the Quantum Spin Hall Transition in Z2 Network Model
Abstract
We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the critical exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a value for the critical exponent ν = 2.73 ± 0.02 that is consistent with that for topologically trivial symplectic systems.
- Publication:
-
Localisation 2011 - Proceedings of the Satellite Conference of LT 26. Edited by Kettemann Stefan. Published by World Scientific Publishing Co. Pte. Ltd
- Pub Date:
- October 2013
- DOI:
- 10.1142/9789814436861_0013
- Bibcode:
- 2013loca.book..114K
- Keywords:
-
- 71.30.+h;
- 73.20.Fz;
- Metal-insulator transitions and other electronic transitions;
- Weak or Anderson localization