A Dirac-material-inspired non-linear electrodynamic model

We propose and study the properties of a non-linear electrodynamics (ED) that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in the work of Keser et al (2022 Phys. Rev. Lett. 128 066402). In the particular regime of a strong magnetic and a weak electric field, it reduces to the photonic non-linear model worked out by Keser et al (2022 Phys. Rev. Lett. 128 066402). We pursue our investigation of the proposed model by analyzing properties of the permittivity and permeability tensors, the energy-momentum tensor and wave propagation effects in presence of a uniform magnetic background. It is shown that the ED here presented exhibits the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy, considering still the presence of a uniform external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a screened Coulomb-like potential with an effective electric charge that runs with the external magnetic field but, as expected for Dirac-type materials, the screening disappears whenever the external magnetic field is switched off.