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In this paper we construct a one-dimensional insulator with an approximatechiral symmetry belonging to the AIII class and discuss its properties. Theconstruction principle is the intentional pollution of the edge of atwo-dimensional quantum spin Hall insulator with magnetic impurities. Theresulting bound states hybridize and disperse along the edge. We discuss underwhich circumstances this chain possesses zero-dimensional boundary modes on thelevel of an effective low-energy theory. The main appeal of our construction isthe independence on details of the impurity lattice: the zero modes are stableagainst disorder and random lattice configurations. We also show that in thepresence of Rashba coupling, which changes the symmetry class to A, one canstill expect localized half-integer boundary excess charges protected by mirrorsymmetry although there is no nontrivial topological index. All of the resultsare confirmed numerically in a microscopic model.

Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator