Simulating and Detecting the Quantum Spin Hall Effect in Kagom\'{e} Optical Lattice

TL;DR

This paper models a transition from quantum spin Hall to normal insulator in a Kagomé lattice, proposing an experimental scheme using ultracold atoms to simulate and detect this topological phase change.

Contribution

It introduces a Kagomé lattice model with spin-orbit coupling and a dimer Hamiltonian, and proposes a novel experimental detection method in ultracold atom systems.

Findings

The model predicts a transition between topological and trivial insulators.

Laser-induced gauge fields can generate the necessary spin-orbit coupling.

The spin Chern number can be directly measured via atomic density profiles.

Abstract

We propose a model which includes a nearest-neighbor intrinsic spin-orbit coupling and a dimer Hamiltonian in the Kagom\'{e} lattice and promises to host the transition from the quantum spin Hall insulator to the normal insulator. In addition, we design an experimental scheme to simulate and detect this transition in the ultracold atom system. The lattice intrinsic spin-orbit coupling is generated via the laser-induced-gauge-field method. Furthermore, we establish the connection between the spin Chern number and the spin-atomic density which enables us to detect the topological quantum spin Hall insulator directly by the standard density-profile technique used in the atomic systems.