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Topological electric quadrupole is a recently proposed concept that extendsthe theory of electric polarization of crystals to higher orders. Such aquadrupole phase supports topological states localized on both edges andcorners. In this work, we show that in a quadrupole phase of honeycomb lattice,topological helical edge states and pseudo-spin-polarized corner states appearby making use of a pseudo-spin degree of freedom related to point groupsymmetry. Furthermore, we argue that a general condition for emergence ofhelical edge states in a (pseudo-)spinful quadrupole phase is mirror ortime-reversal symmetry. Our results offers a way of generating topologicalhelical edge states without spin-orbital couplings.

Helical Topological Edge States in a Quadrupole Phase