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

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 $\nu$ 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 $Z_2$ 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.

arXiv comment12 pages, 13 figures, selected for an Editors' Suggestion in PRB

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Cited by in corpus (33)

• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Anderson Transitions
• Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Network Models of Photonic Floquet Topological Insulators
• Entanglement Negativity at Measurement-Induced Criticality
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Weak (anti-)localization in doped Z_2-topological insulator
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Symmetries of multifractal spectra and field theories of Anderson localization
• Criticality of the metal-topological insulator transition driven by disorder
• Disorder induced transitions in resonantly driven Floquet Topological Insulators
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Thermal metal-insulator transition in a helical topological superconductor
• Topologically Protected Extended States in Disordered Quantum Spin-Hall Systems without Time-Reversal Symmetry
• Disordered Chern insulator with a two step Floquet drive
• Absence of Localization in Disordered Two Dimensional Electron Gas at Weak Magnetic Field and Strong Spin-Orbit Coupling
• The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality
• Anti-localization of graphene under substrate electric field
• Metal--topological-insulator transition in the quantum kicked rotator with Z2 symmetry
• Exact exponents for the spin quantum Hall transition in the presence of multiple edge channels
• Conductance distributions in disordered quantum spin-Hall systems
• Transport through the network of topological channels in HgTe based quantum well
• Localized surfaces of three dimensional topological insulators
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
• Conductance Distribution in Disordered Quantum Wires with a Perfectly Conducting Channel
• Critical exponent for the quantum spin Hall transition in Z_2 network model
• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons