Multichannel dc Josephson effect in ballistic point contacts

Mesoscopic Josephson junctions of small diameter are expected to display universal behavior of the critical current if the junction is short enough so that only one bound Andreev state per transverse channel contributes to the current. For example, the critical current of a clean superconducting-normal-metal-superconducting (SNS) junction is supposed to increase stepwise with the number N of filled transverse channels in the junction, in units of e Delta(0)/(h) over bar. The critical current then is independent of the specific junction geometry. We investigate the robustness of this universal behavior for heterogeneous clean metallic S1NS3 junctions. For this purpose, we present the current-phase relationship in terms of the ratio Delta(1)/Delta(3) for the single-particle s-wave energy gaps of the two superconductors, and in terms of the junction length L and temperature T. If L=0 still holds, finite T and finite asymmetry Delta(1)/Delta(3)<1 reduce the step height of the critical current steps but preserve the sharp step edges. The step behavior is however smeared due to finite L/xi, where xi is the coherence length of the superconductor with the larger gap. The steps are blurred even more at finite temperature, even though L/xi much less than 1 may still hold. On the other hand, junction asymmetry may reduce this smearing for fixed L/xi and T considerably. The limit of a smoothly increasing I-c(N) is recovered for N>N-c, where N-c=min[(1/2)(pi xi/L)(2), (1+Delta(3)/Delta(1))(2), (1/2)pi k(F) xi] for T=0 and L/pi xi much less than 1.