co nd - m at / 9 80 53 78 28 M ay 1 99 8 Magnetic field dependence of the critical current in stacked Josephson junctions

Modulation of the critical current across layers, I c (H), of stacked Josephson junctions (SJJs) as a function of an applied magnetic field parallel to the junction planes is studied theoretically and experimentally for different junction lengths and coupling parameters. It is shown that the I c (H) patterns of long SJJs are very complicated without periodicity in H. This is due to interaction between junctions in the stack. This, in turn, gives rise to the existence of multiple quasi-equilibrium Josephson fluxon modes and submodes which are different with respect to the symmetry of the phase and the fluxon sequence in SJJs. The critical current of long SJJs is multiple valued and is governed by switching between energetically close fluxon modes/submodes. Due to this, the probability distribution of the critical current may become wide and may consist of multiple maxima each representing a particular mode/submode. Experimentally, multiple branched I c (H) patterns and multiple maxima in the I c probability distribution were observed for Bi 2 Sr 2 CaCu 2 O 8+x intrinsic SJJs, which are in a good agreement with numerical simulations and support the idea of having different quasi-equilibrium fluxon modes/submodes in intrinsic SJJs. INTRODUCTION. Properties of stacked Josephson junctions (SJJs) are of great interest both due to possible applications and from the general scientific point of view. A particular interest to SJJs was stimulated by the discovery of high-T c superconductors (HTSC). It is well known that the HTSC compounds have a layered structure with superconducting properties mainly confined to the Cu-O layers. Strong experimental evidence for that was provided by the observation of the intrinsic Josephson effect [1], which is attributed to Josephson coupling between atomic scale superconducting layers. However, it is far from being totally understood. For example, the superconducting 'gap' obtained from measurements of the intrinsic Josephson effect [1,2] is about two times smaller than that determined from ARPES [3] and tunnel measurements [4]. Furthermore, unambiguous observations of AC as well as DC Josephson effects remain to be obtained. In this paper we study theoretically and experimentally the modulation of the critical current across layers, I c (H), of SJJs in a magnetic field parallel to the junction planes. Due to the fluxoid quantization the critical current of the Josephson junction (JJ) should exhibit the well known periodic 'Fraunhofer' modulation of I c (H) in parallel magnetic field, see e.g. Ref. [5], with periodicity …