Localized Topological States in Finite Non-Hermitian Photonic Lattices

Edge states hybridize in finite-size topological materials, opening a gap between edge states which weakens the topological protection. Recent studies discover the recovery of zero modes in the finitesize non-Hermitian Su-Schrieffer-Heeger photonic lattices, which is of significance for fault-tolerant photonic integrations. In this paper, we reveal that the underlying mechanism is level attraction, a phenomenon common in non-Hermitian systems. To present that the level-attraction mechanism is generic for finite topological photonic lattices, we apply biased non-Hermitian potentials on the two-dimensional Qi-Wu-Zhang model and a second-order Bernevig-Hughes-Zhang model based on the spatial distribution of edge states, and demonstrate the evolution of edge states as the potential strength changes. The condition of decoupling the hybridized edge states is that the ratio between hybridization strength and biased non-Hermitian potential strength approaches zero; otherwise, the edge states remain coupled if non-Hermitian potential is small even when the zero real energy is recovered. The results show that the level-attraction mechanism recovers localized zero modes in all these finite-size topological models, and disorder only causes distribution fluctuations of localized edge states. Therefore, in the finite-size regime, zero modes are enhanced or protected by the level-attraction mechanism, offering a strategy for designing compact topological photonic devices.