SELF-SIMILAR MAGNETORESISTANCE OF A SEMICONDUCTOR SINAI BILLIARD

We investigate the transition to a Sinai geometry by introducing a cir cular pattern at the center of a square mesoscopic billiard defined in a high quality AlGaAs/GaAs crystal. The transition induces a novel qu antum interference structure in the magnetoresistance with a character istic field scale over an order of magnitude smaller than previously r eported in mesoscopic billiards. A systematic comparison of fine and c oarse structures, which differ by an order of magnitude in field scale , demonstrates the first observation of geometry-induced ''self-simila rity'' in the magnetoresistance of a semiconductor system.