Rapid Exploration of Topological Band Structures Using Deep Learning

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explo...

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Main Authors:	Vittorio Peano, Florian Sapper, Florian Marquardt
Format:	article
Language:	EN
Published:	American Physical Society 2021
Subjects:	Physics QC1-999
Online Access:	https://doaj.org/article/349701d04dea497cb64ffacaf14e9f84
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id	oai:doaj.org-article:349701d04dea497cb64ffacaf14e9f84
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spelling	oai:doaj.org-article:349701d04dea497cb64ffacaf14e9f842021-12-02T17:51:32ZRapid Exploration of Topological Band Structures Using Deep Learning10.1103/PhysRevX.11.0210522160-3308https://doaj.org/article/349701d04dea497cb64ffacaf14e9f842021-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021052http://doi.org/10.1103/PhysRevX.11.021052https://doaj.org/toc/2160-3308The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics for arbitrary unit-cell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tight-binding model. The tight-binding model encodes not only the band structure but also the symmetry properties of the Bloch waves. This allows us to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. We demonstrate that our method is also suitable to calculate strong topological invariants, even when (like the Chern number) they are not symmetry indicated. Engineering of domain walls and optimization are accelerated by orders of magnitude. Our method directly applies to any passive linear material, irrespective of the symmetry class and space group. It is general enough to be extended to active and nonlinear metamaterials.Vittorio PeanoFlorian SapperFlorian MarquardtAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021052 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Vittorio Peano Florian Sapper Florian Marquardt Rapid Exploration of Topological Band Structures Using Deep Learning
description	The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics for arbitrary unit-cell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tight-binding model. The tight-binding model encodes not only the band structure but also the symmetry properties of the Bloch waves. This allows us to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. We demonstrate that our method is also suitable to calculate strong topological invariants, even when (like the Chern number) they are not symmetry indicated. Engineering of domain walls and optimization are accelerated by orders of magnitude. Our method directly applies to any passive linear material, irrespective of the symmetry class and space group. It is general enough to be extended to active and nonlinear metamaterials.
format	article
author	Vittorio Peano Florian Sapper Florian Marquardt
author_facet	Vittorio Peano Florian Sapper Florian Marquardt
author_sort	Vittorio Peano
title	Rapid Exploration of Topological Band Structures Using Deep Learning
title_short	Rapid Exploration of Topological Band Structures Using Deep Learning
title_full	Rapid Exploration of Topological Band Structures Using Deep Learning
title_fullStr	Rapid Exploration of Topological Band Structures Using Deep Learning
title_full_unstemmed	Rapid Exploration of Topological Band Structures Using Deep Learning
title_sort	rapid exploration of topological band structures using deep learning
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/349701d04dea497cb64ffacaf14e9f84
work_keys_str_mv	AT vittoriopeano rapidexplorationoftopologicalbandstructuresusingdeeplearning AT floriansapper rapidexplorationoftopologicalbandstructuresusingdeeplearning AT florianmarquardt rapidexplorationoftopologicalbandstructuresusingdeeplearning
_version_	1718379218412240896

Rapid Exploration of Topological Band Structures Using Deep Learning

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