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Delocalization Transition of Disordered Axion Insulator
Mesoscale and Nanoscale Physics · Submitted 26 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The axion insulator is a higher-order topological insulator protected by inversion symmetry. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | 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. | result 0.98 | 0.94 | 0.92 | asserted 1.00 |
| s2 | 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. | method 0.97 | 0.96 | 0.07 | asserted 0.94 |
| s3 | We find the localization length critical exponent near the delocalization transition to be $\nu=1.42\pm 0.12$. | result 1.00 | 0.97 | 0.09 | asserted 1.00 |
| s4 | We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. | result 1.00 | 0.95 | 0.10 | asserted 1.00 |
| s5 | We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low energy k$\cdot$p expansion. | contribution 0.55 | 0.96 | 0.03 | asserted 1.00 |
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The paper
Original 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.
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How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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Recently, the higher-order topological insulators (HOTIs) are introduced as a novel topological state [ref] .
Bulk-boundary correspondence in disordered higher-order topological insulators · Introduction · 0.99
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Particularly interesting examples of these phases are first [ref] and higher order [ref] topological insulators, which, in certain cases, only require disorder to preserve the clean limit symmetries on average [ref] , rendering them particularly robust and appealing for applications.
Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states · Introduction · 0.85
What it cites · 3 sentences without a confident label
Cites as background 2 papers
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However, such analyses do not explore the effect of disorder on bulk states, and do not generalize to the topological states protected by generic crystalline symmetries [ref] , such as higher-order topological insulators [ref] .
Antiferromagnetic topological insulators · Introduction · 0.81
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We expect the delocalization transitions to be studied in the recently proposed axion insulator materials [ref] in the future.
M\"{o}bius Insulator and Higher-Order Topology in MnBi$_{2n}$Te$_{3n+1}$ · Introduction · 0.90
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