Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

Abstract

The energy spectrum for the problem of 8-Pmmn borophene's electronic carriers under perpendicular incidence of electromagnetic waves is studied without the use of any perturbative technique. This allows to study the effects of very strong fields. To obtain the spectrum and wavefunctions, the time-dependent Dirac equation is solved by using a frame moving with the space-time cone of the wave, i.e., by transforming the equation into an ordinary differential equation in terms of the wave-phase, leading to an electron-wave quasiparticle. The limiting case of strong fields is thus analyzed.The resulting eigenfunctions obey a generalized Mathieu equation,i.e., of a classical parametric pendulum. The energy spectrum presents bands, and a gap at the Fermi energy. The gaps are due to the space-time diffraction of electrons in phase with the electromagnetic field, i.e., electrons in borophene acquire an effective mass under strong electromagnetic radiation