Two-dimensional anisotropic non-Hermitian Lieb lattice

TL;DR

This paper investigates a two-dimensional anisotropic non-Hermitian Lieb lattice with gain and loss, revealing unique topological edge and corner states influenced by non-Hermiticity and magnetic flux, with potential experimental realizations.

Contribution

It introduces a novel anisotropic non-Hermitian Lieb lattice model with topological edge and corner states, demonstrating how non-Hermiticity affects state localization and topology.

Findings

Active and dissipative topological edge states along different directions.

Non-Hermiticity can switch the corner state location.

Gapless phase characterized by exceptional points configurations.

Abstract

We study an anisotropic two-dimensional non-Hermitian Lieb lattice, where the staggered gain and loss present in the horizontal and vertical directions, respectively. The intra-cell nonreciprocal coupling generates magnetic flux enclosed in the unit cell of the Lieb lattice and creates nontrivial topology. The active and dissipative topological edge states are along the horizontal and vertical directions, respectively. The two-dimensional non-Hermitian Lieb lattice also supports passive topological corner state. At appropriate magnetic flux, the non-Hermiticity can alter the corner state from one corner to the opposite corner as the non-Hermiticity increases. The gapless phase of the Lieb lattice is characterized by different configurations of exceptional points in the Brillouin zone. The topology of the anisotropic non-Hermitian Lieb lattices can be verified in many experimental platforms including the optical waveguide lattices, photonic crystals, and electronic circuits.