Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions

2008/05/31 by Hideaki Obuse, Akira Furusaki, Shinsei Ryu +1 · 47 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Electrical resistivity and conductivity #Electron #Fractal #Geometry #Mathematics #Metal–insulator transition #Multifractal system #Phase transition #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Scaling #Topological Materials and Phenomena #Topological insulator #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.78.115301

published in Physical Review B 78(11) (American Physical Society) · 12 pages, 13 figures, selected for an Editors' Suggestion in PRB

openalex publication_date 2008/09/02 · arxiv created 2008/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation symmetry is broken. The critical exponent \ensuremathν that characterizes the diverging localization length and the bulk multifractal scaling exponents that characterize the amplitudes of the critical wave functions at the metal-insulator transition do not depend on the topological nature of the insulating state, i.e., whether it is topologically trivial (ordinary insulator) or nontrivial (a ℤ₂ insulator supporting a quantum spin Hall effect). This is not true of the boundary multifractal scaling exponents, which we show (numerically) to depend on whether the insulating state is topologically trivial or not.

Citations

• Boundary multifractality in critical one-dimensional systems with long-range hopping
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Exact Relations between Multifractal Exponents at the Anderson Transition
• Quantum Spin Hall Effect in Graphene
• Fractal Geometry: Mathematical Foundations and Applications.
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Conformal invariance and universality in finite-size scaling
• Percolation, quantum tunnelling and the integer Hall effect
• Spin-Orbit Interaction and Magnetoresistance in the Two Dimensional Random System
• Magnetic properties of Sr₂Fe₁+xMo₁-xO₆ with -1 <= x <= 0.25

Cited by

• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons
• Exact Exponents for the Spin Quantum Hall Transition in the Presence of Multiple Edge Channels
• Disordered Chern insulator with a two-step Floquet drive

Related

• Corner multifractality for reflex angles and conformal invariance at 2D Anderson metal–insulator transition with spin–orbit scattering
• Quantum Hall criticality in an amorphous Chern insulator
• Quantum phase transition from a paramagnetic Anderson insulating state to a ferromagnetic many-body localized state via an intermediate ferromagnetic metallic phase
• Fracton Critical Point in Higher-Order Topological Phase Transition
• Boundary criticality in two-dimensional interacting topological insulators