COHERENT MAGNETOTRANSPORT IN CONFINED ARRAYS OF ANTIDOTS .1. DISPERSION-RELATIONS AND CURRENT DENSITIES

The energy band structure of an antidot array defined in a strip geome try of finite width is calculated as a function of the magnetic field, in a parameter range typical of existing experiments, and with edge a spects explicitly taken into account. The calculations are based on a hybrid recursive Green-function technique specially adapted to problem s of this type. The current densities associated with representative B loch states are calculated and visualized. At a given Fermi energy and in zero magnetic field, the set of propagating Bloch states consists of fast states with essentially one-dimensional laminar type flow, cha nneling between rows of antidots, and slower ones with a genuinely two -dimensional flow of vortex character. Simple physical arguments are u sed to explain the existence of the different types of states. At low magnetic fields much of the character of the zero-field states is reta ined. At magnetic fields sufficiently high that the classical cyclotro n diameter is close to the lattice constant of the array the magnetoba nds correspond to edge states and to states of the ''runaway'' type, i n which electrons bounce off antidots in consecutive unit cells. Surpr isingly, states corresponding to electrons in classical orbits pinned around single antidots play only a minor role. With a further-increase of the magnetic field, essentially only edge states survive. In this high-field regime, states beyond the edge states only exist in narrow energy bands, and these states correspond to bulk transport with elect rons hopping between quasilocalized states.