Giant Josephson current through a single bound state in a superconducting tunnel junction.

We study the microscopic structure of the Josephson current in a single-mode tunnel junction with a wide quasiclassical tunnel barrier. In such a junction each Andreev bound state carries a current of magnitude proportional to the amplitude of the normal electron transmission through the junction. Tremendous enhancement of the bound state current is caused by the resonance coupling of superconducting bound states at both superconductor-insulator interfaces of the junction. The possibility of experimental observation of the single bound state current is discussed. Typeset using REVTEX 1 The Josephson effect in a tunnel junction deals with coherent transmission of Cooper pairs through a tunnel barrier which separates superconducting electrodes. What is the mechanism of such a transmission? Conventional theory of the Josephson effect [1,2], based on the phenomenology of the transfer Hamiltonian model [3], does not provide adequate physical description of this process, e.g. similar to the quantum mechanical picture of tunneling of normal electrons. Instead, it treats tunneling as a perturbative transition, introducing a matrix element of coupling of electrons in different electrodes proportional to the amplitude of single electron tunneling [4]. A more realistic description of Josephson tunneling, based on the Bogoliubov-de Gennes equation [5], was suggested by Furusaki and Tsukada [6]. The crucial role in this picture is played by superconducting bound states, similar to Andreev bound states in SNS junctions [7]. A bulk supercurrent, when approaching the tunnel interface, experiences transformation into current flowing through superconducting bound states which provide transmission of Cooper pairs through the barrier. The bound states are induced in the vicinity of the junction by the discontinuity of the superconducting phase, and they appear as a consequence of the current [8]. In a quantum junction the bound state spectrum consists of a single pair of levels per transverse mode, with symmetric position of the levels with respect to the chemical potential. The Josephson current is distributed among bound states in such a way that each bound state carries a current proportional to the normal electron transparency of the junction. In this Letter we show that the above picture of quantization of the Josephson coupling is valid only for an extremely narrow barrier, and that the picture is qualitatively different for any realistic tunnel barrier with large width on an atomic scale. In the latter case, the structure of the bound state spectrum is determined by the coupling of superconducting surface states situated at the two SI interfaces of the SIS junction. In a symmetric junction, the resonance coupling of these surface states provides tremendous enhancement of the current flowing through a single bound state, the magnitude being proportional to the amplitude rather than the probability of normal electron tunneling. The currents are 2 distributed among the bound states in such a way that they almost cancel each other in equilibrium, giving rise to a comparatively small residual current, including the contribution from the continuum. This current coincides with the conventional Josephson current given by Ambegaokar-Baratoff theory [2]. The large current of the single bound state can be revealed under nonequilibrium conditions when the bound level population is imbalanced by means of microwave pumping or tunnel injection. We consider for the sake of clarity a single mode quantum constriction with a rectangular potential barrier of length L and height V (Fig. 1). The structure is described by the 1D Bogoliubov-de Gennes equation [5]: