Ballistic electron transport in lateral antidot arrays investigated by scattering-matrix method

Abstract

A scattering-matrix method is formulated for the study of ballistic electron transport in a lateral quantum system. It is shown that the physically important and less localized states are allowed to dominate in the implementation of the formalism and, therefore, the method remains numerically stable. As an example of its application, the method has been used to study electron transport in both weakly and strongly modulated one-dimensional antidot arrays defined in a two-dimensional electron-gas (2DEG) constriction. For the arrays with a weak modulation, we show that the conductance bands can appear at the edges of the conductance plateaux of the 2DEG constriction. For the arrays with a strong modulation, a more complicated conductance structure has been found. The conductance at high Fermi energies is seen to be characterized by two kinds of fluctuations, namely slow and rapid fluctuations. The slow fluctuations result from wave interferences in a form of Bragg reflections, while the rapid fluctuations reflect the formation of electron minibands. However, due to strong overlaps between the minibands, regular miniband formation may only be observed in the low Fermi energy range.