TRANSPORT IN QUASI-2-DIMENSIONAL SYSTEMS UNDER A WEAK MAGNETIC-FIELD

We calculate the weak-localization correction to the conductivity in a quasi-two-dimensional system. This is done using the condition of weak disorder in the plane epsilon(f) tau >> HBAR. We include the possibility of strong scattering along the anisotropy axis a, i.e., the possibility that t(z) tau < HBAR, where t(z) is the characteristic energy for the coupling along z. The Fermi surface is then diffusive along z (DFS), as opposed to the usual propagative Fermi surface (PFS). As in previous studies on quasi-one-dimensional systems, we: show that this kind of disorder introduces a strong contribution of a purely two-dimensional path to the conductivity. Consequently, these systems cannot be described as simply three-dimensional anisotropic, in opposition to what was supposed in previous experimental study on GaAs-GaxAl1-xAs superlattices. Compared to the quasi-one-dimensional case, the quasi-two-dimensional case allows a complete mathematical treatment in the presence of a weak magnetic field orthogonal to the plane of the layers, and even going beyond the diffusion approximation. We then obtain formulas describing the continuous transition between purely two- and three-dimensional behavior, this with and without a magnetic field.