Designer Edge States in Fractional Polarization Insulators

We theoretically investigated the topological-protected edge states (TESs) in an anisotropic honeycomb lattice with mirror and chiral symmetries, characterized by an alternative topological invariant - fractional polarization (FP), rather than the conventional Chern number. This system termed an FP insulator is a potential platform for edge-state engineering due to its disconnected TESs. These disconnected and robust TESs are susceptible to perturbative chiral symmetry-breaking terms which can generate various patterns including the vanishing helical, spin-polarized, and chiral TESs. Moreover, helical and chiral TES can be achieved by the finite size effect, not possible from the aforementioned terms alone. The demonstration of these various TES in an FP-insulator offers an alternative route in designing reconfigurable two-dimensional nanoelectronic devices.