Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection

TL;DR

This paper explores the formation and evolution of exceptional point loops in a non-Hermitian Lieb lattice, revealing their topological properties, symmetry protections, and potential experimental realizations.

Contribution

It uncovers the formation of an astroid-shaped exceptional point loop due to non-Hermitian chiral symmetry and analyzes their topological robustness and evolution with increasing non-Hermiticity.

Findings

EP loop forms an astroid shape from a triple degeneracy point.

EP loops expand, split, and contract with increasing non-Hermiticity.

Discrete EPs and loops exhibit anisotropic behaviors and topological robustness.

Abstract

An astroid-shaped loop of exceptional points (EPs), comprising four cusps, is found to spawn from the triple degeneracy point in the Brillouin zone (BZ) of a Lieb lattice with nearest-neighbor hoppings when non-Hermiticity is introduced. The occurrence of the EP loop is due to the realness of the discriminant which is guaranteed by the non-Hermitian chiral symmetry. The EPs at the four cusps involve the coalescence of three eigenstates, which is the combined result of the non-Hermitian chiral symmetry and mirror-T symmetry. The EP loop is exactly an astroid in the limit of an infinitesimal non-Hermiticity. The EP loop expands from the $M$ point with increasing non-Hermiticity and splits into two EP loops at a critical non-Hermiticity. The further increase of non-Hermiticity contracts the two EP loops towards and finally to two EPs at the $X$ and $Y$ points in the BZ, accompanied by the emergence of Dirac-like cones. The two EPs vanish at a larger non-Hermiticity. The EP loop disappears and several discrete EPs are found to survive when next-nearest hoppings are introduced to break the non-Hermitian chiral symmetry. A topological invariant called the discriminant number is used to characterize their robustness against perturbations. Both discrete EPs and those on the EP loop(s) are found to show anisotropic asymptotic behaviors. Finally, the experimental realization of the Lieb lattice using a coupled waveguide array is discussed.