Self-similar conductance fluctuations in a Sinai billiard with a mixed chaotic phase space

Abstract

We have investigated ballistic transport through a sub-micron-sized Sinai billiard fabricated using a high-mobility two-dimensional electron gas. The geometry of the billiard is defined by a circular surface gate surrounded by an outer square gate with two quantum point contacts. When both gates are biased negatively, the Sinai billiard is formed and collisions with the confining potential walls generate chaotic classical motion. Recent experiments have revealed novel ‘self-similar’ fluctuation patterns in the conductance of the Sinai billiard, measured as a function of magnetic field perpendicular to the plane of the electron gas. We have undertaken quantum mechanical calculations of the device conductance using a detailed model for the potential landscape under 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.