Scattering-matrix method for ballistic electron transport: Theory and an application to quantum antidot arrays.

Abstract

In this paper we present a scattering-matrix formalism to study electron transport in a mesoscopic system such as a lateral antidot array with a strong modulation potential. We show that the physically important and less localized states are allowed to dominate in the implementation of the formalism and, therefore, the problem of the numerical instability that one often encounters in the application of the transfer-matrix method to lateral electron transport has been solved. As an example of its application, the formalism is used to calculate the electron transmission in one-dimensional (1D) antidot arrays defined in a narrow two-dimensional electron-gas (2DEG) constriction. We show that when the modulation potential of antidots is weak the conductance bands can appear at the edges of the conductance plateaus of the narrow 2DEG constriction. In the case of strong modulation the calculated conductance of the 1D antidot arrays are seen to be characterized by two kinds of strong fluctuations, namely, the slow and rapid fluctuations, in high Fermi-energy range. The slow fluctuations result from wave interferences and the formation of the electron minigaps in the arrays and are insensitive to the temperature up to a few Kelvin, while the rapid fluctuations reflect the formation of the electron minibands and can be easily smoothed out by thermal averaging. Due to strong overlaps between the minibands associated with different 1D paths in the strongly modulated antidot arrays, the effects of the regular miniband formation may only be observed in the low Fermi-energy range, even at very low temperature.