# Dynamical band gap tuning in Weyl semi-metals by intense elliptically polarized normal illumination and its application to $8-Pmmn$ borophene

## TL;DR

This paper investigates how intense elliptically polarized light can dynamically modulate the band gap in Weyl semimetals, specifically applying the findings to $8-Pmmn$ borophene, using a non-perturbative Floquet approach.

## Contribution

It introduces a non-perturbative method to predict dynamical gap formation in Weyl semimetals under elliptically polarized light, applicable to various materials.

## Key findings

- Derived the quasienergy spectrum using Mathieu equations.
- Identified conditions for dynamical gap formation and stability.
- Estimated electromagnetic parameters for gap tuning in borophene.

## Abstract

The Dynamical-gap formation in Weyl semimetals modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schr\"odinger equation for the Weyl Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasi-energy spectrum of the two-dimensional Weyl Hamiltonian under normal incidence of elliptically polarized electromagnetic waves are obtained using a non-perturbative approach. In it, the Weyl equation is reduced to an ordinary second-order differential Mathieu equation. It is shown that the stability conditions of the Mathieu functions are directly inherited by the wave function resulting in a quasiparticle spectrum consisting of bands and gaps determined by dynamical diffraction and resonance conditions between the electron and the electromagnetic wave. Estimations of the electromagnetic field intensity and frequency, as well as the magnitude of the generated gap are obtained for the $8-Pmmn$ phase of borophene. We provide with a simple method that enables to predict the formation of dynamical-gaps of unstable wave functions and their magnitudes. This method can readily be adapted to other Weyl semimetals.