A theoretical study of a π-junction realized in a quantum dot array

We have studied theoretically the Josephson effect through a quantum dot array connected with two superconducting electrodes. The dot array has been studied by two models: (1) a Hubbard chain with boundary pair-potentials and (2) an Anderson impurity model coupled to superconducting leads. The first model shows a parity effect. Namely, the system becomes a pi-junction for odd N-e or a 0-junction for even N-e, where N-e is the average number of electrons in the array. By shifting the on-site potential at the dot array, N-e increases one by one for finite U. The maximum Josephson current shows peaks of resonant tunneling determined by both the parity effect and the Hubbard gap. In order to consider the Josephson effect at finite temperature, we have generalized the quantum Monte Carlo method by Hirsch and Fye and have applied it to the second model with a quantum dot, which shows occurrence of the Coulomb blockade, (C) 2002 Elsevier Science B.V. All rights reserved.