Assembling topological insulators with lasers

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 ($α_{\bf k}$, with ${\bf k}$ being the momentum) is reversed in every alternating wires as $\pmα_{\bf k}$. 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.

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