Computing spectral properties of topological insulators without artificial truncation or supercell approximation Article Swipe

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Matthew J. Colbrook , Andrew Horning , Kyle Thicke , Alexander B. Watson ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1093/imamat/hxad002

Topological insulators (TIs) are renowned for their remarkable electronic properties: quantized bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in the presence of material defects and disorder. Computations of these physical properties generally rely on artificial periodicity (the supercell approximation, which struggles in the presence of edges), or unphysical boundary conditions (artificial truncation). In this work, we build on recently developed methods for computing spectral properties of infinite-dimensional operators. We apply these techniques to develop efficient and accurate computational tools for computing the physical properties of TIs. These tools completely avoid such artificial restrictions and allow one to probe the spectral properties of the infinite-dimensional operator directly, even in the presence of material defects, edges and disorder. Our methods permit computation of spectra, approximate eigenstates, spectral measures, spectral projections, transport properties and conductances. Numerical examples are given for the Haldane model, and the techniques can be extended similarly to other TIs in two and three dimensions.

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Computation Truncation (statistics) Eigenvalues and eigenvectors Supercell Operator (biology) Boundary (topology) Boundary value problem Mathematics Topology (electrical circuits) Statistical physics Applied mathematics Computer science Physics Mathematical analysis Algorithm Quantum mechanics Biochemistry Repressor Transcription factor Gene Telecommunications Radar Chemistry Combinatorics Statistics

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Type: article
Language: en
Landing Page: https://doi.org/10.1093/imamat/hxad002
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Cited By: 9
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DOI: https://doi.org/10.1093/imamat/hxad002

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Title: Computing spectral properties of topological insulators without artificial truncation or supercell approximation

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Publication year: 2023

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Publication date: 2023-01-31

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Authors: Matthew J. Colbrook, Andrew Horning, Kyle Thicke, Alexander B. Watson

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Landing page: https://doi.org/10.1093/imamat/hxad002

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Concepts: Computation, Truncation (statistics), Eigenvalues and eigenvectors, Supercell, Operator (biology), Boundary (topology), Boundary value problem, Mathematics, Topology (electrical circuits), Statistical physics, Applied mathematics, Computer science, Physics, Mathematical analysis, Algorithm, Quantum mechanics, Biochemistry, Repressor, Transcription factor, Gene, Telecommunications, Radar, Chemistry, Combinatorics, Statistics

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Cited by: 9

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Citations by year (recent): 2025: 4, 2024: 2, 2023: 2, 2022: 1

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