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

Abstract

The Dynamical-gap formation in Weyl semimetals modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schrödinger 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.

10 pages, 7 figures

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• Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmn borophene: The role of different frequency, temperature and scattering limits
• Electron transitions for Dirac Hamiltonians with flat-bands under electromagnetic radiation and its application to the $\alpha -{\mathcal{T}}_3$ graphene model
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities
• Oblique and asymmetric Klein tunneling across smooth NP junctions or NPN junctions in 8-Pmmn borophene
• Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones
• Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: monodromy matrix approach
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Electronic states bound by repulsive potentials in graphene irradiated by a circularly polarized electromagnetic field
• Dirac materials under linear polarized light: quantum wave function evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields