Superluminal Spacetime Crystals Induced by Anomalous Velocity Modulation

Time-modulated media offer powerful opportunities for controlling light, yet extending such concepts to optical frequencies has remained challenging. Here we propose a different route to photonic spacetime crystals based on modulation of the anomalous velocity in low-symmetry conductors, particularly Weyl semimetals. We show that when driven by a strong optical pump, the anomalous velocity of Bloch electrons induces an ultrafast spacetime modulation that propagates with a superluminal phase velocity relative to the dielectric background. This self-induced modulation enables unidirectional light transport below the optical gap and, near the epsilon-near-zero point, gives rise to collective parametric resonance and stimulated emission of volume plasmons. These findings identify Weyl semimetals as a promising platform for realizing optical spacetime crystals and open a pathway toward active and nonreciprocal photonic systems governed by quantum geometric effects.