Andreev resonances in quantum ballistic transport in SNS junctions  A. Ingerman a, * , J. Lantz a , E. Bratus' b , V. Shumeiko a , G. Wendin a a Chalmers University of Technology and G oteborg University, 41296 G oteborg, Sweden b B.Verkin Institute for Low Temperature Physics and Engineering, 310164 Kharkov, Ukraine Abstract We report the results of an investigation of the eect of the superconducting bound states on coherent multiple Andreev re¯ections in quantum SNS junctions. A rich resonant structure of the current, associated with the bound states and consisting of peaks, onsets and oscillations, is found by numerical calculations. Positions of the current structures are not given by subharmonics of the energy gap but rather determined by the junction geometry. We present analytical classi®cation of the resonant current structures and calculate their positions and amplitudes. We show that the resonant current structures in three-terminal SNS interferometers can be controlled by external magnetic ¯ux. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.50.+r; 74.80.Fp; 74.20.Fg; 73.23.Ad Keywords: Voltage biased Josephson junction; Multiple Andreev re¯ection; SNS junction; Ballistic transport; Mesoscopic superconductivity Ballistic SNS junctions are interesting meso- scopic structures where the eect of Andreev bound states on the current transport can be ac- curately studied. Recent experiments on ballistic SNS junctions fabricated with high mobility 2DEG [1±4] revealed unusual features in the voltage dependence of the dierential resistance, which were tentatively attributed to Andreev reso- nances. Such features have been observed neither in metallic break junctions nor in diusive SNS junctions. The current in metallic break junctions is accurately described by the theory of coherent multiple Andreev re¯ections MAR) [5,6] where the eect of Andreev bound states is completely neglected. This description is adequate because of the small atomic) size of these junctions. In 2DEG devices, the junction size is typically comparable to the superconducting coherence length, and the Andreev bound states are well developed. This will lead to pronounced resonant features in the multi- particle currents. On the other hand, in diusive junctions, the Andreev bound levels are washed out into a continuum spectrum and the current resonances diminish to the level of mesoscopic ¯uctuations incoherent MAR). We present a study of the eect of Andreev bound states on the current transport in ballistic SNS junctions. We will focus on quantum junc- tions where the resonant eects are most pro- nounced, however, the results can be extended to plane junctions with large number of weakly coupled Physica C 352 2001) 77±81 www.elsevier.nl/locate/physc * Corresponding author. E-mail address: ingerman@fy.chalmers.se   A. Ingerman). 0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII:S0921-453400)01698-1