Dynamic moir'e-like band modulation in Dirac materials via multi-beam optical interference

We propose a purely optical Floquet framework to dynamically generate moiré-like superlattices and quasicrystalline potentials in a gapped Dirac material, entirely bypassing the need for physical twisting. The interference of three coherent circularly polarized beams produces a triangular, valley-dependent Floquet mass landscape that folds the Dirac spectrum into a mini-Brillouin zone, driving pronounced valley-selective miniband reconstruction. We further show that the bands near the Fermi level undergo a light-driven topological phase transition. Remarkably, interfering five or seven beams yields non-crystallographic spatial patterns, giving rise to optical quasicrystals with similar valley contrasting features. Although this purely optical approach provides a versatile route to band engineering, reaching deep subwavelength modulation requires overcoming the free-space diffraction limit. To overcome this limitation, we consider highly confined, linearly polarized surface plasmon polariton fields with controlled relative phases. Their phase-controlled interference generates a spatially alternating chiral mass with zero spatial average. Consequently, the two valleys exhibit degenerate energy spectra while hosting opposite valley-resolved miniband Chern numbers. Our findings establish a reconfigurable, all-optical platform for dynamically engineering moiré-like bands, quasicrystalline electronic states, and valley-dependent topology without mechanical twisting.