A physical explanation for the origin of self-similar magnetoconductance fluctuations in semiconductor billiards

We report quantum-mechanical calculations which replicate the self-similar magnetoconductance fluctuations observed in recent experiments on semiconductor Sinai billiards. We interpret these fluctuations by considering the mixed stable-chaotic classical dynamics of electrons in the billiard. In particular, we show that the fluctuation patterns are dominated by individual stable orbits. The scaling characteristics of the self-similar fluctuations depend on the geometry of the associated stable orbit. We find that our analysis is insensitive to the details of the potential landscape, and is applicable to real devices with a wide range of soft-wall profiles. We show that our analysis also provides a possible explanation for the distinct series of magnetoconductance fluctuations observed in recent experiments on carbon nanotubes.