Scattering of edge states in quasi-one-dimensional periodic systems

We develop an integral equation Green's function method to study the transmission of waves (in two dimensions) through a continous potential in the presence of a perpendicular magnetic field. Motivated by recent experiments, the general formalism is then applied to compute the magnetoconductance of a two-dimensional system containing a finite number of barriers confined by a parabolic potential. When the magnetic field is strong and there are practically only one or two uncoupled edge states, we predict approximate periodic conductance oscillations in qualitative agreement with those observed. The periodic and the total number of oscillations within a miniband is determined by commensurability of the pertinent length scales (magnetic length, lattice constant and electron wave length) as well as by the size of the system. For weak magnetic fields, the number of edge states increases, but the effect of coupling between modes is evaluated and proves to be small.