Radu P. Lungu

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

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.

TWO-DIMENSIONAL ELECTRON SYSTEM IN ELECTROMAGNETIC RADIATION FIELD

We consider a two-dimensional electron gas in the presence of a monochromatic linear polarized electromagnetic field, within the Floquet formalism. The Floquet states have a simple relation with the energy eigenstates in the absence of the field. Therefore the single-particle and the two-particle Green functions of the many-body system with Coulomb interactions, in the radiation field, can be formally calculated by the standard diagrammatic techniques, as for the conservative system. We derive the elementary excitations of quasi-particle type, the plasma dispersion relation, and the ground state quasi-energy, and we relate them to the corresponding results for the conservative system.