Topological Transition in Aromatic and Quinonoid π-Conjugated Polymers Induced by Static Strain

A topological quantum phase transition has been identified for the first time for 24 π-conjugated polymers as a function of external longitudinal strain due to a level crossing of the frontier orbitals at the topological phase transition. Topological phase is determined by the presence/absence of edge states. Out of the 24 polymers 15 are traditionally assigned an aromatic character, and 9 are traditionally assigned a quinonoid character. We find that all aromatic ones correspond to the trivial topological phase (Zak invariant, Z₂ = 0), while all of the quinonoid ones to the nontrivial topological phase (Z₂ = 1) replacing the intuitive characterization of aromatic/quinonoid with the physically well-defined Zak invariant. Unique topological phase transition as a function of tensile strain can be achieved for four of the quinonoid ones. Tensile strain in these cases leads to a reduction of the bandgap. We introduced a figure of merit for indicating the efficiency of achievable very small bandgap upon the application of external strain.