Band structure for relativistic charged particles immersed in a structurally chiral electromagnetic field

In this paper, we determine the band structure of an electromagnetic space-time crystal. We construct a coordinate transformation in which the matrix elements of the Dirac equation are constant. Consequently, their corresponding band structure is recovered analytically. The band structure is fragmented into three different energy regions. In the center, there is a region prohibited for all particles (universal band gap), which is symmetrically enveloped by two energy regions of the same width. These regions allow the passage of particles with a specific spin (discriminatory band gaps). Furthermore, we demonstrate that, through the appropriate combination of the refractive index, the length of the electromagnetic wave, and the amplitude of the electric field, it is possible to shorten the bandwidth of the universal gap and replace it with a discriminatory band gap. In that sense, the proposed system constitutes an alternative procedure to observe the Schwinger mechanism experimentally.