https://doi.org/10.1140/epjb/e2004-00145-6
Josephson effect between superconducting nanograins with discrete energy levels
Sektion Physik and CeNS,
Ludwigs-Maximilians-Universität München,
Theresienstr. 37, 80333 München, Germany
Corresponding author: a gobert@lmu.de
Received:
2
May
2003
Revised:
8
September
2003
Published online:
28
May
2004
We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting 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 approximation 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
