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

References in corpus (14)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological Transition in a Non-Hermitian Quantum Walk
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• On the topological immunity of corner states in two-dimensional crystalline insulators

Cited by in corpus (1)

• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices