Electron transitions for Dirac Hamiltonians with flat-bands under electromagnetic radiation and its application to the $\alpha -{\mathcal{T}}_3$ graphene model

Abstract

In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency $\Omega$. When a flat band is present two kinds of resonant transitions are found. Considering the $\alpha -{\mathcal{T}}_3$ graphene model as a minimal model with a flat band and Dirac cones, and describing the dynamics using the interaction picture, we study the band transitions induced by an external electromagnetic field. We found that transitions depend upon the relative angle between the electron momentum and the electromagnetic field wave vector. For parallel incidence, the transitions are found using Floquet theory while for other angles perturbation theory is used. In all cases, the transition probabilities and the frequencies are found. For some special values of the parameter $\alpha$ or by charge doping, the system behaves as a three level or a two-level Rabi system. All these previous results were compared with numerical simulations. A good agreement was found between both. The obtained results are useful to provide a quantum control of the system.

8 pages, 5 figures

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Cited by in corpus (10)

• Unconventional phases in a Haldane model of dice lattice
• Dynamical Floquet spectrum of Kekulé-distorted graphene under normal incidence of electromagnetic radiation
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Tunable valley filtering in dynamically strained $\alpha$-${\mathcal{T}}_3$ lattices
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: monodromy matrix approach
• Thermal Transport Properties of Magnons on the $\alpha$-T${}_3$ Lattice
• Flat bands without twists: periodic holey graphene
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Superconductivity and geometric superfluid weight of a tunable flat band system