Critical exponent for the quantum spin Hall transition in Z_2 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 $\nu =2.73\pm 0.02$ that is consistent with that for topologically trivial symplectic systems.

5 pages, 4 figures, submitted to the proceedings of Localisation 2011

References in corpus (8)

• Critical exponent for the quantum Hall transition
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• Finite Size Scaling Analysis of the Anderson Transition
• The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality
• Conductance distributions in disordered quantum spin-Hall systems
• Transport properties in network models with perfectly conducting channels

Cited by in corpus (5)

• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Disordered weak and strong topological insulators
• Criticality of the metal-topological insulator transition driven by disorder
• Algebraic and Geometric Mean Density of States in Topological Anderson Insulators
• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons