Coherent magnetotransport in confined arrays of antidots. I. Dispersion relations and current densities

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Abstract
The energy band structure of an antidot array defined in a strip geometry of finite width is calculated as a function of the magnetic field, in a parameter range typical of existing experiments, and with edge aspects explicitly taken into account. The calculations are based on a hybrid recursive Green-function technique specially adapted to problems of this type. The current densities associated with representative Bloch 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, channeling between rows of antidots, and slower ones with a genuinely two-dimensional flow of vortex character. Simple physical arguments are used to explain the existence of the different types of states. At low magnetic fields much of the character of the zero-field states is retained. At magnetic fields sufficiently high that the classical cyclotron diameter is close to the lattice constant of the array, the magnetobands correspond to edge states and to states of the ‘‘runaway’’ type, in which electrons bounce off antidots in consecutive unit cells. Surprisingly, 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 electrons hopping between quasilocalized states. © 1996 The American Physical Society.