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.

Resonant Tunneling Controlled by Laser and Constant Electric Fields

“…On the other hand elements of the B ′ matrix can be evaluated by substituting a general solution (8) to the expression (6) and applying the continuity condition to it at x i−1 . After some algebraic manipulations we obtain the following equation,…”

“…Vector potential is periodic in time and describes a laser field. Such conditions are met for example in semiconductor nanostructures [1][2][3][4][5][6][7][8] (like quantum wires or wells), carbon nanotubes [9,10] or in surface physics [11][12][13][14][15]. To make our presentation as clear as possible we shall restrict ourself to the one-space-dimensional case, although extension of this algorithm to two and threespace dimensional systems, also with magnetic field accounted for, is possible (see, e.g.…”