Assembling topological insulators with lasers

TL;DR

This paper proposes a laser-based optical lattice device with alternating spin-orbit coupling to realize a $Z_2$ topological insulator, restoring time-reversal symmetry and enabling protected edge states detection.

Contribution

It introduces a novel optical lattice setup with alternating SO coupling to engineer intrinsic $Z_2$ topological insulators using existing tools.

Findings

The device achieves a non-trivial $Z_2$ topological phase.

It restores global time-reversal symmetry in the lattice.

Edge states can be detected via non-local current measurements.

Abstract

Despite the realizations of spin-orbit (SO) coupling and synthetic gauge fields in optical lattices, the associated time-reversal symmetry breaking, and 1D nature of the observed SO coupling pose challenges to obtain intrinsic $Z_2$ topological insulator. We propose here a model optical device for engineering intrinsic $Z_2$ topological insulator which can be easily set up with the existing tools. The device is made of a periodic lattice of quantum mechanically connected atomic wires (dubbed SO wires) in which the laser generated SO coupling ($\alpha_{\bf k}$, with ${\bf k}$ being the momentum) is reversed in every alternating wires as $\pm\alpha_{\bf k}$. The associated small Zeeman terms are also automatically reversed in any two adjacent SO wires, which allow to effectively restore the global time-reversal (TR) symmetry. Therefore, the two SO wires serve as the TR partner to each other which is an important ingredient for $Z_2$ topological insulators according to the Kane-Mele model. These properties ensure a non-trivial $Z_2$ invariant topological insulator phase with protected edge states. We also discuss that a non-local current measurement can be used to detect the chiral edge states.