Transport signatures of symmetry protection in one-dimensional topological insulators

The unique feature of any topological insulator is presence of gapless states on its boundaries. In one dimension these states live on the edges and are protected against symmetry-preserving local perturbations. Here we describe a scheme for probing the robustness of the edge states by calculating the transport characteristics of an array of dimers attached to external leads. Numerical results obtained from non-equilibrium Green's function theory will be presented. It will be shown that there is a drop in the differential conductance as the dimer array is perturbed by a local symmetry-breaking perturbation, while the drop is strongly suppressed if the symmetries are maintained. A brief analytic description will be provided in support of the numerics. Both types of 1D topological insulators, conventional time-independent and periodically-driven (Floquet), are considered.