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Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities

The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schrödinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under the normal incidence of linearly polarized waves are obtained for an arbitrarily intense electromagnetic radiation. We applied a set of unitary transformations to reduce the Schrödinger equation to an ordinary second-order differential Hill equation with complex coefficients. Through the stability analysis of this differential equation, the weak and strong field regimes are clearly distinguished in the quasi-spectrum. In the weak electric field regime, above a certain threshold given by the field parameters, the spectrum mostly resembles that of free electrons in graphene. Below this threshold, in the strong electric field regime, the spectrum abruptly becomes highly anisotropic and a gap opens up. As an example, we apply the results to the particular case of borophene.