Simulating a Chern Insulator with C = ±2 on Synthetic Floquet Lattice

The synthetic Floquet lattice, generated by multiple strong drives with mutually incommensurate frequencies, provides a powerful platform for quantum simulation of topological phenomena. In this study, we propose a 4-band tight-binding model of the Chern insulator with a Chern number C = ±2 by coupling two layers of the half Bernevig–Hughes–Zhang lattice and subsequently mapping it onto the Floquet lattice to simulate its topological properties. To determine the Chern number of our Floquet-version model, we extend the energy pumping method proposed by Martin et al. [2017 Phys. Rev. X 7 041008] and the topological oscillation method introduced by Boyers et al. [2020 Phys. Rev. Lett. 125 160505], followed by numerical simulations for both methodologies. The simulation results demonstrate the successful extraction of the Chern number using either of these methods, providing an excellent prediction of the phase diagram that closely aligns with the theoretical one derived from the original bilayer half Bernevig–Hughes–Zhang model. Finally, we briefly discuss a potential experimental implementation for our model. Our work demonstrates significant potential for simulating complex topological matter using quantum computing platforms, thereby paving the way for constructing a more universal simulator for non-interacting topological quantum states and advancing our understanding of these intriguing phenomena.