$SU(3)$ Topological Insulators in the Honeycomb Lattice

TL;DR

This paper explores how $SU(3)$ spin-orbit coupling in honeycomb optical lattices with spin-1 bosons can produce topologically non-trivial band structures and edge states, revealing topological transitions driven by lattice geometry.

Contribution

It demonstrates that $SU(3)$ spin-orbit coupling can break time-reversal symmetry and induce topological phases in honeycomb lattices, unlike $SU(2)$ couplings.

Findings

$SU(3)$ couplings lead to non-trivial Chern numbers

Edge states appear in strip geometries

Topological transitions occur by varying a parameter

Abstract

We investigate realizations of topological insulators with spin-1 bosons loaded in a honeycomb optical lattice and subjected to a $SU(3)$ spin-orbit coupling - a situation which can be realized experimentally using cold atomic gases. In this paper, we focus on the topological properties of the single-particle band structure, namely Chern numbers (lattice with periodic boundary conditions) and edge states (lattice with strip geometry). While $SU(2)$ spin-orbit couplings always lead to time-reversal symmetric Hubbard models, and thereby to topologically trivial band structures, suitable $SU(3)$ spin-orbit couplings can break time reversal symmetry and lead to topologically non-trivial bulk band structures and to edge states in the strip geometry. In addition, we show that one can trigger a series of topological transitions (i.e. integer changes of the Chern numbers) that are specific to the geometry of the honeycomb lattice by varying a single parameter in the Hamiltonian.