Dirac quasiparticles in acoustic lattices: A platform for relativistic topological space-time crystal

We explore two-dimensional Dirac quasiparticles in acoustic space-time crystals formed by coherently propagating surface acoustic waves (SAWs). Recent experiments show that SAWs on piezoelectric substrates can induce dynamic chiral gauge fields in graphene. By superposing multiple SAWs traveling in orthogonal directions, we create a space-time periodic “acoustic lattice” that traps Dirac quasiparticles into Landau-like orbits and drags them along the wave. A key insight arises from the Lorentz symmetry of the Dirac equation: in the comoving frame of the SAW, the gauge field becomes static, and the quasiparticle experiences a periodic magnetic texture. This provides a simple picture for the tilted minibands observed in the laboratory frame. Using a Floquet-Bloch approach, we derive the miniband structure and show that the effective hopping between Landau orbitals acquires complex, SAW-controlled phases. In certain regimes, the lowest miniband is isolated, nearly flat, and topologically nontrivial, characterized by a finite Chern number. Our results establish moving acoustic lattices as a versatile platform for Floquet engineering and topological control of relativistic quasiparticles.