Coherent magnetotransport in confined arrays of antidots. II. Two-terminal conductance

The magnetoconductance due to coherent transport through antidot arrays in confined (strip) geometries is investigated. Our hybrid Green-function method is adapted to the calculation of the transport properties of such systems. A simple derivation of the surface Green function in a magnetic field is provided. The two-terminal conductance of antidot arrays is analyzed on the basis of their magnetoband structure. At relatively low magnetic fields the conductance (in units of 2${\mathit{e}}^2$/h) approximately follows the number of states (NOS) of the corresponding infinite structure, with a steplike oscillatory dependence on the magnetic field superimposed onto a slow background variation. The Fourier power spectra of the magnetoconductance and NOS curves reveal that the periodicity is related to the basic Aharonov-Bohm frequency of the system. Around the field value at which the cyclotron diameter equals the lattice constant of the array, the magnetoresistance has a broad maximum. Also at about a quarter of this field value a broad maximum can be detected. These results agree with experimental findings. The broad maxima are usually attributed to resonances with electron states trapped around single and groups of four antidots. An alternative interpretation, in better agreement with the facts, is proposed. At high fields, simple edge state transport at the boundaries of the array takes over. © 1996 The American Physical Society.