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 reveal a bulk-edge-corner correspondence, such that $n$-th 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. We introduce an unsupervised approach -- physics-graph-informed machine learning (PGIML) -- to enhance the data mining ability of machine learning with limited domain knowledge. Through PGIML, we experimentally demonstrate the second-order NHSE in a two-dimensional non-Hermitian topolectrical circuit. 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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• Dimensional transmutation from non-Hermiticity
• Topological Phases in Magnonics
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Photonic corner skin modes
• Zoology of non-Hermitian spectra and their graph topology
• Non-Hermitian Squeezed Polarons
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Universal platform of point-gap topological phases from topological materials
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Experimental observation of exceptional bound states in a classical circuit network
• Anomalous fractal scaling in two-dimensional electric networks
• A brief review of hybrid skin-topological effect
• Percolation-induced PT symmetry breaking
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Kinked linear response from non-Hermitian cold-atom pumping
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
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• Engineering topological states and quantum-inspired information processing using classical circuits
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• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
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• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Exceptional second-order topological insulators
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes