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.
KAUST Repository Item: Exported on 2022-11-16
Acknowledged KAUST grant number(s): 2022-CRG10-4660
Acknowledgements: C.S., P.H., X.Za., X.Zh., K.N.S., and U.S. acknowledge funding from King Abdullah University of Science and Technology (KAUST) under Award 2022-CRG10-4660. S.L., R.S., and T.J.C. acknowledge the National Key Research and Development Program of China under grant nos. 2017YFA0700201, 2017YFA0700202, and 2017YFA0700203. C.H.L. acknowledges the Singapore MOE Tier I grant WBS: R-144-000-435-133. R.T. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 258499086-SFB 1170 and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (ct.qmat Project-ID 390858490-EXC 2147). S.Z. acknowledges the Research Grants Council of Hong Kong (AoE/P-701/20 and 17309021).