New SubmissionBAND STRUCTURE FOR RELATIVISTIC ELECTRONS IMMERSED IN A CHIRAL ELECTROMAGNETIC FIELD

Despite the current importance of the Dirac equation in the study of quantum mechanics and high-energy physics, it is reported in the literature that the number of analytical solutions for this equation is very scarce. In this poster, we present a new physical system in which the Dirac equation presents an analytical solution.

The system under study consists of a spacetime crystal formed by interacting a circularly polarized electromagnetic wave with a relativistic electron in a dispersive medium characterized by a refractive index n. For the study of the crystal, a coordinate system was constructed that transforms the matrix elements of the Dirac equation into constants, consequently, the band structure of the crystal is analytically soluble.

The band structure of the system is fragmented into three 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, which is understandable step by step due to the analytical nature of the solution, 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, which is understandable step by step due to the analytical nature of the solution.