Physica C 235-240 (1994)3315-3316 PRYS~CA North-Holland Paramagnetic field cooled susceptibility in superconducting loops with Josephson junctions. C. Auletta, P. Caputo, G. Costabile, R. De Luca, S. Pace, A. Saggese Department of Physics University of Salerno, 84100 Salerno Italy By the analysis of the potential energy of a single loop interrupted by one Josephson junction, we show that a paramagnetic field-cooled susceptibility can appear in this simple system. Recently, the discovery of a paramagnetic effect in high-Tc sintered polycrystals in the low field region [1] has opened new questions about the superconducting state. In fact, the Meissner effect in metallic superconductors is stricly related to the coherence of a gauge invariant macroscopic phase; thus, this paramagnetic behavior should change, at least qualitatively, the classical microscopic description. In this paper we propose an explanation for the experimentally observed paramagnetic Meissner effect with a traditional approach by considering a superconducting ring interrupted by Josephson junctions. Indeed, this system is the simplest junction array model describing granular superconductors. The Gibbs potential energy for a single loop with N Josephson junctions (JJ's) in series is given by [2]: N (I) ((I) -- (I)ex,) 2 G=EC °(1-cos k)+ k=~ 2zr 2L , (1) where I ° is the maximum Josephson current of the k-thjunction, ~0 is the magnetic quantum flux, q~k is the gauge invariant superconducting phase difference across the k-th JJ, ~ext=l.loHS is the geometrical flux of the applied magnetic field H, S being the total area of the system, and L is the effective inductance of the loop. The total flux can be expressed as follows: = 4~ext + LI. (2) The superconducting phase difference is linked to the flux trapped in the ring by the fluxoid quantization condition: N k=a (ok + 2 tr'~-7 = 2 a'nI' (3) where nf is an integer. Eq.1 for N = 1 reduces to the equation of the energy for a if-squid [2]. We first consider the simplest case of only one junction in the loop. We study the stationary magnetic states of this system after field cooling by finding the absolute minimum of the energy G with respect to the flux ~, for each fixed value of ~exr" Fig.1 shows the behavior of the flux A~, defined as the difference between the flux tl~min at the absolute minimum point of G and ~ex,, as a function of the external flux Iff~ex t for different values of the parameter fl(T) = 27rLI ° (T)/O 0 . 0.5 ' ' ' I ' ' ' I ' ' ' J3=1 <l 0 -0.5 , , , I , , ~ I , ~ , 0 1 m.~. / ~ 2 3 ext 0 Figure 1. Normalized flux difference ~min in terms of the applied flux for different values of ft. 0921-4534D4/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0921-4534(94)02223-2