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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Autores principales: Vittorio Peano, Florian Sapper, Florian Marquardt
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Publicado: American Physical Society 2021
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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
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