Topological Zero-Energy Domain-Wall States in Generalized Su-Schrieffer-Heeger and Kitaev Chains Beyond the Topological Classification

Conventional belief is that the Altland-Zirnbauer tenfold classification table for topological insulators and superconductors determines the existence of zero-energy topological states. We demonstrate zero-energy topological domain-wall states in classes thought to be forbidden using representative one-dimensional generalized Su-Schrieffer-Heeger (SSH) and Kitaev chains. The tight-binding and topological field theory indicates zero-energy domain-wall states robust to disorder emerges. A low-energy effective approach and SU(N) transformations simplifies the effective Hamiltonians into a form equivalent to SSH and Kitaev chains. Finally, we show the Berry curvature for the generalized SSH and Kitaev chains and that the respective Berry phase difference of neighboring domains are quantized. The quantized Berry phase difference indicates a general bulk-boundary principle, protecting zero-energy topological states.