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

Ce Shang, Shuo Liu, Ruiwen Shao, Peng Han, Xiaoning Zang, Xiangliang Zhang, Khaled N. Salama, Wenlong Gao, Ching Hua Lee, Ronny Thomale, Aurélien Manchon, Shuang Zhang, Tie Jun Cui, Udo Schwingenschlögl

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
Pages (from-to)2202922
JournalAdvanced science (Weinheim, Baden-Wurttemberg, Germany)
DOIs
StatePublished - Nov 13 2022

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