  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.
