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Yung Kim1,2, Minwook Kyung1,2, Hee Chul Park3, Kyungmin Lee1,2, Jung-Wan Ryu3, Moon Jip Park3, and Bumki Min2

1 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea 2 Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea3 Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS) Daejeon, 34126, Republic of Korea

Higher-order Hopf-link skin effects in non-Hermitian circuits

Topological properties of a system can be classified by quantifying a discretized invariant. For systems describable with one-dimensional non-Hermitian Hamiltonians, a winding number can be evaluated by experimentally reconstructing knots or braids of complex eigenenergy strings. While nontrivial winding of a non-Hermitian band has recently been demonstrated in a one-synthetic-dimensional photonic system, a topological phase transition and its corresponding physical manifestation in real and momentum space have not been visualized yet. Moreover, dimensional extension and generalization of the concept have yet to be accomplished. For the first time, we report here the visualization of linking and unlinking of a Hopf fiber in momentum space of a two-dimensional non-Hermitian circuit and show comcomittant emergence of a higher-order skin effect in real space. We anticipate that the proposed non-Hermitian platform and the visualization methodology may provide an interesting testbed for the investigation and classification of non-Hermitian topology.

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