Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: Monodromy matrix approach

摘要

We analyze the quasiencrgy spectrum, the valence to conduction-band transition probabilities, and the photo-induced density currents of a tilted anisotropic Dirac material subject to linearly and circularly polarized electromagnetic fields. The quasienergy spectrum is numerically calculated from the monodromy matrix of the Schrodinger equation via the Floquet theorem for arbitrarily intense electromagnetic fields. The monodromy matrix method developed here is much more efficient for obtaining the evolution operator and Floquet spectrum of time-driven systems than the traditional diagonalization using replicas, as this last method requires truncation in both the number of replicas and system size. To assess the valence to conduction-band transition limes, we deduced a Rabi-like formula in the rotating wave approximation. In the strong-field regime, the spectrum as a function of the momentum components divides into two very distinctive regions. In the first, located around the Dirac point, the quasi spectrum is significantly distorted by the field as the electronic parameters are renormalized by electronic dressing. In the second, all the characteristics of the free carrier spectrum are retained. Linearly polarized light anisotropically deforms the spectrum according to the field polarization direction. Dirac-like points form around the original Dirac point. The quasi spectrum of circularly polarized light, instead, exhibits a gap formation in the Dirac point and has elliptical symmetry. We show that, in contrast to the single-photon resonant transitions that characterize the weak-field regime, the strong-field regime is dominated by multiphoton resonances. These processes also manifest themsel ves in the generation of high harmonics in the density current.