Chaotic electron motion in macroscopic and mesoscopic antidot lattices

Antidot arrays consisting of a lattice of nanometer scale holes etched through a two-dimensional electron gas display distinct resistance anomalies if the period of the array is much smaller than the electron mean free path. While in conventional conductors the electrons are deflected by randomly distributed scatterers, the situation is different in antidot arrays: here, the electrons predominantly collide with the periodically arranged antidots. Due to their geometry, antidot lattices can be considered as periodically repeated Sinai billiards, known for their classically chaotic electron dynamics. Here, electron transport through two different types of antidot lattices will be discussed: in macroscopic antidot lattices the extent of the array is much larger than the phase coherence length or the elastic mean free path of the electrons while in mesoscopic ones the electrons can travel ballistically from the ‘entrance’ to the ‘exit’ of the array.