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

TL;DR

This paper introduces a non-Hermitian second-order topological insulator model with $ abla_{3}$ clock symmetry, demonstrating the emergence of parafermion corner states, and realizes these states in electric circuits.

Contribution

It presents a novel non-Hermitian topological model with parafermion corner states and extends the concept to $ abla_{4}$ and $ abla_{6}$ symmetries on different lattices.

Findings

Topological corner states are identified as parafermions.

Parafermion corner states are observed in electric circuit experiments.

Models for $ abla_{4}$ and $ abla_{6}$ parafermions are constructed.

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.