Role of long-range interactions in one-dimentional non-Hermitian topological photonic systems

We study topological phonon polaritons (TPhPs) in one-dimensional dimerized silicon carbide nanoparticle chains. While the topological property of longitudinal modes is like the conventional Hermitian Su-Schrieffer-Heeger (SSH) model, for transverse modes, we find a topological phase transition at a substantially large lattice constant, due to the presence of long-range non-Hermitian interactions in an infinitely long chain. On the other hand, in the finite chain, due to these interactions, the edge and bulk modes become hybridized. In this situation, the non-Hermitian skin effect, i.e., the emergence of localized bulk modes over the edges, leads to the breakdown of bulk-boundary correspondence. By considering this effect and subsequently proposing a modified complex Zak phase for a finite chain, the topological behavior of the conventional SSH model is still recovered. Our study provides profound implications to the fields of non-Hermitian topological physics and quantum mechanical models with long-range interactions.