s __ __ !B 1 December 1997 ELSEWIER Physics LettersA 236 (1997) 120-124 PHYSICS LETTERS A Stability of regular orbits in ballistic quantum dots Y. Okubo a, Y. Ochiai a, D. Vasileska b, R. Akis b, D.K. Ferry b, J.l? Bird ‘, K. Ishibashi c, Y. AoyagiC, T. Suganoc a zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Department of Materials Science, Chiba University, 1-33 Yayoi-cho Inage-ku. Chiba 263, Japan h Center for Solid State Electronics Researchand Department of Electrical Engineering. Arizona State Universip, Tempe, AZ 85287-5706, USA c Nanoelectronic Materials Laboratory, Frontier Research Program, RIKEN, 2-1 Hirosawa, Saitama 351-01, Japan Received 30 May 1997;revisedmanuscript received 19 August 1997; accepted for publication 21 August 1997 Communicated by L.J. Sham zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR Abstract We study experimentally and theoretically a mesoscopic quantum billiard in which the classical dynamics is expected to be chaotic. However, we find that the magnetotransport is dominated by a periodic oscillation, characteristic of regular orbits in the structure, indicating stability of the stable, non-chaotic classical trajectories. @ 1997 Elsevier Science B.V. Mesoscopic semiconductor billiards have recently attracted considerable interest as a novel experimental probe of transport, and quantumchaos, on the quan- tum and semi-classical scale [ l-51. While precise de- tails differ from experiment to experiment, the devices used in these studies are typically a central meso- scopic cavity, which is connectedto externalreser- voirs throughwhich the current and conductance can be measured. The centralcavity itself is lithographi- cally defined and its size is smaller than fundamental transport scales such as the mean free path. Electron interference in these structures is an important pro- cess and strongly influencestheir resulting electrical behavior.While it hasbeen suggested that multiple billiard scattering from the cavity walls will induce chaotic behavior [ 6,7], recent studiesof rectangular cavities have established the basic regularnatureof the orbits [ 5,8]. In stadium billiards, it is still thought that chaotic behavior is induced even in open sys- tems [ 1,2,9- 111. Simulations,however,suggest that wave function scarring due to the existence of regular orbits can occur even in the stadium structure [ 121. Recently,numerical studies of a multi-disc scattering systemhave shownthatsignificant numbers of trajec- tories follow almost exclusively one of the stableor- bits leading to the conclusion that the stable RAM tori tend to resist breakup into chaos evenin this system. In this Letter,we compare experimental and theoretical results for a ballistic stadium in which there are many re-entrant curvesin the defining geometry(much like a multi-disc system) and in which the classical dy- namics is therefore expectedto be chaotic. We find that there are quite stable trajectories which lead to regular, periodic oscillations in the magnetoconduc- tance,suggesting that the stable RAM tori are indeed seenexperimentally. Split-gate quantum dots were fabricated in GaAs/AlGaAs heterojunctions using standard litho- graphic techniques. Prior to gate deposition, optical lithography was used to define a Hallbar patternin the wafers, allowing electrical contact to be made to the two-dimensionalelectron gas below the sur- 037%9601/97/$17.00 @ 1997 Elsevier Science B.V. All rights reserved. PII SO375-9601(97)00674-9