Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning

Abstract Topological phases of matter are conventionally characterized by the bulk‐boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d − 1)‐dimensional boundary states. By extension, higher‐order topological insulators r...

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Main Authors: Ce Shang, Shuo Liu, Ruiwen Shao, Peng Han, Xiaoning Zang, Xiangliang Zhang, Khaled Nabil Salama, Wenlong Gao, Ching Hua Lee, Ronny Thomale, Aurélien Manchon, Shuang Zhang, Tie Jun Cui, Udo Schwingenschlögl
Format: Article
Language:English
Published: Wiley 2022-12-01
Series:Advanced Science
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Online Access:https://doi.org/10.1002/advs.202202922
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author Ce Shang
Shuo Liu
Ruiwen Shao
Peng Han
Xiaoning Zang
Xiangliang Zhang
Khaled Nabil Salama
Wenlong Gao
Ching Hua Lee
Ronny Thomale
Aurélien Manchon
Shuang Zhang
Tie Jun Cui
Udo Schwingenschlögl
author_facet Ce Shang
Shuo Liu
Ruiwen Shao
Peng Han
Xiaoning Zang
Xiangliang Zhang
Khaled Nabil Salama
Wenlong Gao
Ching Hua Lee
Ronny Thomale
Aurélien Manchon
Shuang Zhang
Tie Jun Cui
Udo Schwingenschlögl
author_sort Ce Shang
collection DOAJ
description Abstract Topological phases of matter are conventionally characterized by the bulk‐boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d − 1)‐dimensional boundary states. By extension, higher‐order topological insulators reveal a bulk‐edge‐corner correspondence, such that nth order topological phases feature (d − n)‐dimensional boundary states. The advent of non‐Hermitian topological systems sheds new light on the emergence of the non‐Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher‐order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach—physics‐graph‐informed machine learning (PGIML)—to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second‐order NHSE in a 2D non‐Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk‐boundary correspondence in the second‐order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non‐Hermitian systems.
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spelling doaj.art-5224ad38142e4a97a1641a942c8910d52022-12-29T14:19:17ZengWileyAdvanced Science2198-38442022-12-01936n/an/a10.1002/advs.202202922Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine LearningCe Shang0Shuo Liu1Ruiwen Shao2Peng Han3Xiaoning Zang4Xiangliang Zhang5Khaled Nabil Salama6Wenlong Gao7Ching Hua Lee8Ronny Thomale9Aurélien Manchon10Shuang Zhang11Tie Jun Cui12Udo Schwingenschlögl13King Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955‐6900 Saudi ArabiaState Key Laboratory of Millimeter Waves Southeast University Nanjing 210096 ChinaState Key Laboratory of Millimeter Waves Southeast University Nanjing 210096 ChinaKing Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE) Thuwal 23955‐6900 Saudi ArabiaKing Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955‐6900 Saudi ArabiaKing Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE) Thuwal 23955‐6900 Saudi ArabiaKing Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE) Thuwal 23955‐6900 Saudi ArabiaPaderborn University Department of Physics Warburger Str. 100 33098 Paderborn GermanyDepartment of Physics National University of Singapore Singapore 117551 Republic of SingaporeInstitut für Theoretische Physik und Astrophysik Universität Würzburg 97074 Würzburg GermanyCINaM Aix‐Marseille University CNRS Marseille FranceDepartment of Physics The University of Hong Kong Hong Kong ChinaState Key Laboratory of Millimeter Waves Southeast University Nanjing 210096 ChinaKing Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955‐6900 Saudi ArabiaAbstract Topological phases of matter are conventionally characterized by the bulk‐boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d − 1)‐dimensional boundary states. By extension, higher‐order topological insulators reveal a bulk‐edge‐corner correspondence, such that nth order topological phases feature (d − n)‐dimensional boundary states. The advent of non‐Hermitian topological systems sheds new light on the emergence of the non‐Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher‐order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach—physics‐graph‐informed machine learning (PGIML)—to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second‐order NHSE in a 2D non‐Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk‐boundary correspondence in the second‐order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non‐Hermitian systems.https://doi.org/10.1002/advs.202202922graph visualizationmachine learningnon‐Hermitian circuitskin effecttopology
spellingShingle Ce Shang
Shuo Liu
Ruiwen Shao
Peng Han
Xiaoning Zang
Xiangliang Zhang
Khaled Nabil Salama
Wenlong Gao
Ching Hua Lee
Ronny Thomale
Aurélien Manchon
Shuang Zhang
Tie Jun Cui
Udo Schwingenschlögl
Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
Advanced Science
graph visualization
machine learning
non‐Hermitian circuit
skin effect
topology
title Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
title_full Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
title_fullStr Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
title_full_unstemmed Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
title_short Experimental Identification of the Second‐Order Non‐Hermitian Skin Effect with Physics‐Graph‐Informed Machine Learning
title_sort experimental identification of the second order non hermitian skin effect with physics graph informed machine learning
topic graph visualization
machine learning
non‐Hermitian circuit
skin effect
topology
url https://doi.org/10.1002/advs.202202922
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