Experimental and Theoretical Investigations of Electron Dynamics in a Semiconductor Sinai Billiard

Abstract

We describe a surface gate-defined mesoscopic semiconductor billiard with a square geometry which we can evolve continuously to a Sinai geometry by adjusting the bias on a circular gate located at the centre of the square. We concentrate on clusters of magneto-conductance structure formed on two magnetic field scales, which emerge during the transition from the square to the Sinai geometry. This change in shape is accompanied by a transition from non-chaotic to chaotic electron dynamics, which has been a topic of considerable interest for many years. The observed structure is due to quantum chaotic processes induced by the presence of the circle. Our experimental results agree with classical dynamics simulations which suggest the two field scales are determined by two families of electron trajectories which sample the full geometry and corner sub-geometry. Finally, we report the observation of striking similarities in the structures observed on the two different field scales. This indicates the emergence of self-similarity with the introduction of the circle to the Sinai billiard geometry.