Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator

Abstract

Parafermions are a natural generalization of Majorana fermions. We consider a breathing Kagome lattice with complex hoppings by imposing ${\mathbb{Z}}_3$ clock symmetry in the complex energy plane. It is a non-Hermitian generalization of the second-order topological insulator characterized by the emergence of topological corner states. We demonstrate that the topological corner states are parafermions in the present ${\mathbb{Z}}_3$ clock-symmetric model. It is also shown that the model is realized in electric circuits properly designed, where the parafermion corner states are observed by impedance resonance. We also construct ${\mathbb{Z}}_4$ and ${\mathbb{Z}}_6$ parafermions on breathing square and honeycomb lattices, respectively.

9 pages, 10 figures

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