Scheme to equilibrate the Hall response of topological systems from coherent dynamics

Two-dimensional topologically distinct Chern insulators are separated by gap closing points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experience the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. Here we demonstrate a scheme to equilibrate the quantized Hall response from pure coherent dynamics as the Hamiltonian is slowly tuned from the topologically trivial to nontrivial regimes. We further apply our method to Weyl semimetals in three dimensions and find the equilibrated Hall response despite the underlying gapless band structure. Our finding not only lays the theoretical foundation for observing the Hall response in Chern insulators but also for observing and controlling Weyl semimetals in ultracold atomic gases.