Quantum magnetotransport in a mesoscopic antidot lattice

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Abstract
The effect of a perpendicular magnetic field on quantum electron transport in a periodic array of antidots is studied. On the basis of a recursive Green-function technique the conductance of the finite antidot lattice is calcualted in the framework of the Landauer-Büttiker formalism. The dependence of the conductance of the finite array on the Fermi energy and the magnetic field can be understood from an analysis of the band structure of the corresponding infinite-strip superlattice. The latter is shown to consist of quasiparabolic Bloch states and almost dispersionless bands representing the bulk Landau states and quasibound states around antidots. The particle current density associated with these bands is calculated. The quasiparabolic band corresponds to propagation in magnetic edge states, whereas antidot bands correspond to counterclockwise rotation around single antidots. Landau bands, on the other hand, correspond to the counterclockwise rotation in the space between antidots. It is shown that the particle current flow in Landau and antidot states can have a maximum near the lower edge of the strip, i.e., opposite to that which is normally expected. The physical reason for this is given. The magnetoconductance through the finite array of antidots is shown to exhibit plateaulike behavior when electrons propagate in the magnetic edge state, and irregular oscillating behavior corresponding to propagation in Landau or antidot bands. The latter is due to strong mode mixing at the boundary of the array.