Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry

TL;DR

This paper investigates the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice, revealing a $ ext{Z}_2$ topological insulator phase stabilized by artificial gauge fields and robust against various perturbations.

Contribution

It introduces a detailed topological analysis of a time-reversal invariant Kagome lattice model with spin-orbit coupling and flux, including effects of on-site potentials and staggered fields.

Findings

Identification of a $ ext{Z}_2$ topological insulator phase in the model.

Demonstration of phase stability under spin-flip and on-site potential variations.

Discovery of topological phases at large on-site energies and with staggered potentials.

Abstract

We study the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice. The model is time-reversal invariant and realizes a $\mathbb{Z}_2$ topological insulator as a result of artificial gauge fields. We develop topological arguments to describe this system showing three inequivalent sites in a unit cell and a flat band in its energy spectrum in addition to the topological dispersive energy bands. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. In particular, we also address the situation where on-site energies may differ inside a unit cell. Moreover, a staggered potential on the lattice may realize topological phases for the half-filled situation. Another interesting result is the occurrence of a topological phase for large on-site energies. To describe topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop a mathematical approach, related to smooth fields.