Classical and Quantum Transport in Antidot Arrays

The story of solid state physics is the story of electrons in periodic potentials caused by the periodic arrangement of atoms in crystalline solids. It was early recognized that an additionally imposed periodic potential can significantly modify the solid’s properties [1]. A major breakthrough in this respect was the concept of bandstructure engineering introduced by L. Esaki and R. Tsu [2,3]. The advent of molecular beam epitaxy with the possibility to grow semiconductor crystals atom by atom (see, e.g. [4]) allowed one not only to fabricate such one-dimensional superlattices superimposed upon the three-dimensional crystallographic lattice but also to realize two-dimensional electron systems (2DES) of superior quality [5]. Two-dimensional electron systems offered a wealth of new phenomena and are still the subject of current research. Prominent examples of effects based on the reduction of dimensionality for conduction electrons (or holes), are the quantum Hall effect (QHE) [6] and the fractional quantum Hall effect (FQHE) [7]. New phenomena were also expected for a one- or two-dimensional (2D) periodic potential imposed upon a two-dimensional electron system [8,9]. By using nanolithographic techniques it is possible these days to impress periodic potentials of different strength, period and shape upon high mobility two-dimensional electron systems such that the electron mean free path l e and phase coherence lenght l ø is much longer than the period of the periodic potentials. Two different types of potential landscapes are displayed in Fig. 5.1 showing weak and strong 2D-periodic potentials imposed upon a two-dimensional electron system