Floquet solutions for two-dimensional quasi-free electrons interacting with a monochromatic laser field

Abstract

We consider quasi-free electrons, moving in a two-dimensional lattice, and interacting with a strong monochromatic electromagnetic field; the interaction between each electron and the lattice is considered to be sufficiently weak, so it is possible to treat it as a small perturbation. Using a variant of the stationary perturbation theory in the extended Hilbert space, we have obtained the quasi-energies and the reduced Floquet eigenvectors of a quasi-free electron. The low order perturbation corrections show that the quasi-energy spectra have positive and negative jumps and the Floquet eigenfunctions have generalized Bloch form. These results show some similarities to the corresponding properties of the conservative quasi-free electron model, in the absence of the external radiation field.