Clock-symmetric non-Hermitian second-order topological insulator

Abstract

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 construct topological corner states with the $$\mathbb {Z}_{3}$$ clock-symmetric model. It is also shown that the model is realized in an electric circuit properly designed, where corner states are observed by impedance resonance. We also construct the $$\mathbb {Z}_{4}$$ and $$\mathbb {Z}_{6}$$ symmetric models on breathing square and honeycomb lattices, respectively.