GEOMETRY-INDUCED FRACTAL BEHAVIOR - FRACTIONAL BROWNIAN-MOTION IN A BALLISTIC MESOSCOPIC BILLIARD

We report geometry-induced fractal behaviour analogous to fractional B rownian motion in the low-field magnetoconductance fluctuations of a m esoscopic 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 t he billiard potential profile. Hence, our results constitute a possibl e experimental observation of the infinite hierarchical nature of this mixed phase space. Preliminary investigations into the effects of tem perature and gate bias, which directly control electron coherence and billiard potential profile, are presented. (C) 1998 Elsevier Science B .V. All rights reserved.