SELF-SIMILAR CONDUCTANCE FLUCTUATIONS IN A SINAI BILLIARD WITH A MIXED CHAOTIC PHASE-SPACE

We have investigated ballistic transport through a sub-micron-sized Si nai billiard fabricated using a high-mobility two-dimensional electron gas. The geometry of the billiard is defined by a circular surface ga te surrounded by an outer square gate with two quantum point contacts. When both gates are biased negatively, the Sinai billiard is formed a nd collisions with the confining potential walls generate chaotic clas sical motion. Recent experiments have revealed novel 'self-similar' fl uctuation patterns in the conductance of the Sinai billiard, measured as a function of magnetic held perpendicular to the plane of the elect ron gas. We have undertaken quantum mechanical calculations of the dev ice conductance using a detailed model for the potential landscape und er the surface gates. We compare these results with predictions for a hard-walled billiard and show that the surface gate geometry can have a large effect on the observed transport properties. (C) 1998 Elsevier Science B.V. All rights reserved.