Delocalization Transition of Disordered Axion Insulator

Abstract

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be $\nu =1.42\pm 0.12$. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low energy k$\cdot$p expansion.

arXiv comment8+11 pages, 4+6 figures, some references added

References in corpus (73)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators with Inversion Symmetry
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Weyl Semimetal in a Topological Insulator Multilayer
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Experimental discovery of Weyl semimetal TaAs
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Higher-Order Topological Insulators
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Intrinsic magnetic topological insulators in van der Waals layered MnBi${}_2$Te${}_4$-family materials
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Higher-Order Topology in Bismuth
• Experimental realization of an intrinsic magnetic topological insulator
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Riemannian symmetric superspaces and their origin in random matrix theory
• Inversion Symmetric Topological Insulators
• Dynamical Axion Field in Topological Magnetic Insulators
• Impurity effect on weak anti-localization in the topological insulator Bi2Te3
• Crossover between weak localization and weak antilocalization in magnetically doped topological insulator
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
• Competition between weak localization and antilocalization in topological surface states
• Quantitative mappings between symmetry and topology in solids
• Corrections to scaling at the Anderson transition
• Magnetic Topological Quantum Chemistry
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Tunable Surface Conductivity in Bi2Se3 Revealed in Diffusive Electron Transport
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• The strong side of weak topological insulators
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Tailoring tricolor structure of magnetic topological insulator for robust axion insulator
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Surfaces of Axion Insulators
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Topological non-symmorphic crystalline insulators
• Rare region effects dominate weakly disordered 3D Dirac points
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Dirty Weyl fermions: rare region effects near 3D Dirac points
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• The Anderson transition: time reversal symmetry and universality
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Universal Scaling of Quantum Anomalous Hall Plateau Transition
• Statistical Topological Insulators
• Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals
• Topological states from topological crystals
• Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• The Axion Insulator as a Pump of Fragile Topology
• Anderson localization and the topology of classifying spaces
• Critical Behavior and Universal Signature of an Axion Insulator State
• Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes

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• Critical Behavior and Universal Signature of an Axion Insulator State
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