Designing long and highly conducting molecular wires with multiple nontrivial topological states

Molecular one-dimensional topological insulators (1D TIs), described by the Su-Schrieffer-Heeger (SSH) model, are a new class of molecular electronic wires whose low-energy topological edge states endow them with high electrical conductivity. However, when these 1D TIs become long, the high conductance is not sustained because the coupling between the edge states decreases with increasing length. Here, we present a new design where we connect multiple short 1D SSH TI units linearly or in a cycle to create molecular wires with a continuous topological state density. Using a tight-binding method, we show that the linear system gives a length-independent conductance. The cyclic systems show an interesting odd-even effect, with unit transmission in the topological limit, but zero transmission in the trivial limit. Furthermore, based on our calculations, we predict that these systems can support resonant transmission with a quantum of conductance. We can further expand these results to phenylene-based linear and cyclic 1D TI systems and confirm the length-dependent conductance in such systems.