Fragile Phases as Affine Monoids: Classification and Material Examples

Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. For the first time, we obtain a complete classification of the fragile topologic...

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Autores principales:	Zhi-Da Song, Luis Elcoro, Yuan-Feng Xu, Nicolas Regnault, B. Andrei Bernevig
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/0a173924844c48159658a34176c59982
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spelling	oai:doaj.org-article:0a173924844c48159658a34176c599822021-12-02T16:02:59ZFragile Phases as Affine Monoids: Classification and Material Examples10.1103/PhysRevX.10.0310012160-3308https://doaj.org/article/0a173924844c48159658a34176c599822020-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031001http://doi.org/10.1103/PhysRevX.10.031001https://doaj.org/toc/2160-3308Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. For the first time, we obtain a complete classification of the fragile topological phases, which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure that far surpasses that of stable or strong topological states. We find and enumerate hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues, and we link the mathematical structure of these phases to that of affine monoids in mathematics. Furthermore, for the first time, we predict and calculate (hundreds of realistic) materials where fragile topological bands appear, and we showcase the very best ones.Zhi-Da SongLuis ElcoroYuan-Feng XuNicolas RegnaultB. Andrei BernevigAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031001 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Zhi-Da Song Luis Elcoro Yuan-Feng Xu Nicolas Regnault B. Andrei Bernevig Fragile Phases as Affine Monoids: Classification and Material Examples
description	Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. For the first time, we obtain a complete classification of the fragile topological phases, which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure that far surpasses that of stable or strong topological states. We find and enumerate hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues, and we link the mathematical structure of these phases to that of affine monoids in mathematics. Furthermore, for the first time, we predict and calculate (hundreds of realistic) materials where fragile topological bands appear, and we showcase the very best ones.
format	article
author	Zhi-Da Song Luis Elcoro Yuan-Feng Xu Nicolas Regnault B. Andrei Bernevig
author_facet	Zhi-Da Song Luis Elcoro Yuan-Feng Xu Nicolas Regnault B. Andrei Bernevig
author_sort	Zhi-Da Song
title	Fragile Phases as Affine Monoids: Classification and Material Examples
title_short	Fragile Phases as Affine Monoids: Classification and Material Examples
title_full	Fragile Phases as Affine Monoids: Classification and Material Examples
title_fullStr	Fragile Phases as Affine Monoids: Classification and Material Examples
title_full_unstemmed	Fragile Phases as Affine Monoids: Classification and Material Examples
title_sort	fragile phases as affine monoids: classification and material examples
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/0a173924844c48159658a34176c59982
work_keys_str_mv	AT zhidasong fragilephasesasaffinemonoidsclassificationandmaterialexamples AT luiselcoro fragilephasesasaffinemonoidsclassificationandmaterialexamples AT yuanfengxu fragilephasesasaffinemonoidsclassificationandmaterialexamples AT nicolasregnault fragilephasesasaffinemonoidsclassificationandmaterialexamples AT bandreibernevig fragilephasesasaffinemonoidsclassificationandmaterialexamples
_version_	1718385251887087616

Fragile Phases as Affine Monoids: Classification and Material Examples

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