Helical Topological Edge States in a Quadrupole Phase

TL;DR

This paper demonstrates the existence of topological helical edge states and corner states in a honeycomb lattice quadrupole phase, revealing new ways to realize topological states without spin-orbit coupling.

Contribution

It introduces a mechanism for topological helical edge states in a quadrupole phase using pseudo-spin symmetry, expanding the understanding of topological phases.

Findings

Helical edge states appear in a honeycomb quadrupole phase.

Pseudo-spin polarization is related to point group symmetry.

Mirror or time-reversal symmetry is essential for these states.

Abstract

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 honeycomb lattice, topological helical edge states and pseudo-spin-polarized corner states appear by making use of a pseudo-spin degree of freedom related to point group symmetry. Furthermore, we argue that a general condition for emergence of helical edge states in a (pseudo-)spinful quadrupole phase is mirror or time-reversal symmetry. Our results offers a way of generating topological helical edge states without spin-orbital couplings.