Experimental signatures of 0D topological states in 1D electronic materials: a topical review

One-dimensional (1D) topological insulators provide a minimal setting for bulk-boundary correspondence, hosting symmetry-protected zero-dimensional (0D) end and domain-wall states. This review summarizes the 1D symmetries and topological invariants that protect these modes, and surveys experimental signatures used to identify them, including in-gap spectral weight, spatial localization, robustness to perturbations, and electrical tunability. We contrast engineered and intrinsic platforms, such as atom-by-atom assembled chains, self-organized Peierls systems, on-surface synthesized graphene nanoribbon superlattices, quantum spin Hall edges confined to the 1D limit, and quasi-1D chain materials where crystalline symmetries protect end states. We close with an outlook on electrically controllable end states and device-motivated directions enabled by robust, discrete 0D modes.