Helical Topological Edge States in a Quadrupole Phase

A topological electric quadrupole is a recently proposed concept that extends the theory of electric polarization of crystals to higher orders. Such a quadrupole phase supports topological states localized on both edges and corners. In this work, we show that in a quadrupole phase of a honeycomb lattice, topological helical edge states and pseudospin-polarized corner states appear by making use of a pseudospin degree of freedom related to point group symmetry. Furthermore, we argue that a general condition for the emergence of helical edge states in a (pseudo)spinful quadrupole phase is the existence of either mirror or time-reversal symmetry. Our results offer a way of generating topological helical edge states without spin-orbital couplings.