Emergent non-Hermitian edge polarisation in an Hermitian tight-binding model

We study a bipartite Kronig-Penney model with negative Dirac-delta potentials that may be used, amongst other models, to interpret plasmon propagation in nanoparticle arrays. Such system can mapped into Su-Schrieffer-Heeger-like however, general, the overlap between 'atomic' wavefunctions of neighbouring sites is not negligible. In such case, edge states finite system, which retain their topological protection, appear either attenuated or amplified. This phenomenon, called "edge polarisation", usually associated an underlying non-Hermitian topology. By investigating bulk we show resulting tight-binding eigenvalue problem made this physical (lattice-site) basis. The {\it effective} Hamiltonian possesses ${\cal PT}$-symmetry and its invariant, interpreted terms classification, found given by winding number $\mathbb{Z}$-type. observation polarisation, through established bulk-boundary correspondence, then as emerging skin-effect Hamiltonian. Therefore, matrix generates non-Hermitian-like effects otherwise Hermitian problem; general fact applicable broader range systems than just one studied here.