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

Mesoscale and Nanoscale Physics;Other Condensed Matter