Floquet Engineering of Relativistic Electrons in Propagating Waves and Lorentz symmetry

We investigate the behavior of 3D Dirac electrons subjected to waves propagating through the material, such as laser light, polaritons, acoustic waves, and sliding density waves, each with distinct propagation speeds. These waves, being periodic in both space and time, induce Floquet-Bloch states in the electrons. We classify these waves based on their speed into time-like, light-like, and space-like categories, and identify distinct electronic states in each case. Our study reveals phase transitions in the electronic band structure, leading to the emergence of Floquet Weyl bands, which may become Type-II near the transition points. The impact of Floquet band engineering is amplified by Lorentz contraction, reaching its maximum when the wave speed approaches the Fermi velocity.

Reference: arXiv:2407.21458 (2024)