Emergent Weyl-like points in periodically modulated systems

We investigate a three-dimensional (3D) topological phase resembling a Weyl semimetal, modulated by a periodic potential and engineered through Floquet dynamics. This system is constructed by stacking two-dimensional Chern insulators and hosts Weyl-like points defined in the parameter space $(k_x, k_y, z)$, distinct from conventional Weyl points in momentum space $(k_x, k_y, k_z)$. The Weyl-semimetal-like phase exhibits characteristics akin to those of Weyl semimetals, including linear dispersion near the Weyl-like points, nontrivial bulk topology, the presence of Fermi arcs connecting the Weyl-like points, and the Berry monopoles. Unlike traditional Weyl semimetals, these features manifest in real space rather than momentum space. Furthermore, we calculate the local density of states, the layer Hall conductance, and the total 3D Hall conductivity, demonstrating that the Weyl-semimetal-like phase remains stable under weak and moderate interlayer couplings. The influence of disorder is also examined: Beyond a critical disorder strength, the Weyl-like points destabilize and the topological phase collapses. Moreover, by computing the Floquet Chern number, we demonstrate that the locations of the Weyl-like points can be tuned via high-frequency laser pumping. Finally, we show that both type-I and II Weyl-like behaviors can arise in a tilted Weyl-like model.