DOI: 10.1140/epjb/e2004-00145-6 THE EUROPEAN PHYSICAL JOURNAL B

Abstract. We investigate the Josephson effect between two coupled superconductors, coupled by the tun-neling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk super-conducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approxi-mation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model. PACS. 74.20.-z Theories and models of superconducting state – 74.78.-w Superconducting films and low-dimensional structures – 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects