Semiconductor Billiards - a Controlled Environment to Study Fractals

Fractals describe the scaling properties of a spectacular variety of natural objects. In general, fractal studies in natural environments are "passive" in the sense that there is no experimental interaction with the system being observed. In contrast, in this paper we investigate fractals in an artificial environment where controlled changes in the generation process can be used to study how fractals evolve. To do this we construct micron-sized billiards in high quality semiconductor materials where the properties of chaotic electrons can be tuned with precision. By inserting a circle at the centre of a square billiard, we investigate the transition between two distinct forms of fractals observed in the billiard's conductance - from exact to statistical self-affinity.