Symmetry-protected higher-order exceptional points in staggered flatband rhombic lattices

TL;DR

This paper demonstrates the creation of higher-order exceptional points in PT-symmetric staggered rhombic lattices through non-Hermitian engineering, revealing unique phase transitions, dynamics, and potential for studying topological and nonlinear phenomena.

Contribution

It introduces a novel method to realize higher-order EPs in flatband lattices using non-Hermitian couplings and symmetry protection, expanding the understanding of non-Hermitian topological systems.

Findings

Higher-order EPs can be engineered at BZ boundary and center.

Distinct phase transitions occur with on-site gain/loss and non-Hermitian couplings.

Power dynamics show exponential and quartic increases near EPs.

Abstract

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains as a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in PT -symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also nonHermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform towards the investigation of the higher-order EPs, and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.