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Understanding Topological Insulators in Real Space
A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indi...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8156361/ https://www.ncbi.nlm.nih.gov/pubmed/34067586 http://dx.doi.org/10.3390/molecules26102965 |
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author | Martín Pendás, Angel Muñoz, Francisco Cardenas, Carlos Contreras-García, Julia |
author_facet | Martín Pendás, Angel Muñoz, Francisco Cardenas, Carlos Contreras-García, Julia |
author_sort | Martín Pendás, Angel |
collection | PubMed |
description | A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, [Formula: see text] , also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to [Formula: see text] are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts. |
format | Online Article Text |
id | pubmed-8156361 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-81563612021-05-28 Understanding Topological Insulators in Real Space Martín Pendás, Angel Muñoz, Francisco Cardenas, Carlos Contreras-García, Julia Molecules Article A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, [Formula: see text] , also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to [Formula: see text] are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts. MDPI 2021-05-17 /pmc/articles/PMC8156361/ /pubmed/34067586 http://dx.doi.org/10.3390/molecules26102965 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Martín Pendás, Angel Muñoz, Francisco Cardenas, Carlos Contreras-García, Julia Understanding Topological Insulators in Real Space |
title | Understanding Topological Insulators in Real Space |
title_full | Understanding Topological Insulators in Real Space |
title_fullStr | Understanding Topological Insulators in Real Space |
title_full_unstemmed | Understanding Topological Insulators in Real Space |
title_short | Understanding Topological Insulators in Real Space |
title_sort | understanding topological insulators in real space |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8156361/ https://www.ncbi.nlm.nih.gov/pubmed/34067586 http://dx.doi.org/10.3390/molecules26102965 |
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