Geometry-induced fractal behaviour: Fractional Brownian motion in a ballistic mesoscopic billiard

We report geometry-induced fractal behaviour analogous to fractional Brownian motion in the low-field magnetoconductance fluctuations of a mesoscopic semiconductor billiard. Such fractal behaviour was recently predicted to be due to the trajectory trapping behaviour of the mixed (regular/chaotic) phase space generated by the soft-walled nature of the billiard potential profile. Hence, our results constitute a possible experimental observation of the infinite hierarchical nature of this mixed phase space. Preliminary investigations into the effects of temperature and gate bias, which directly control electron coherence and billiard potential profile, are presented.