Manifestation of geometric effects in temperature behavior of ac magnetic response of Josephson junction arrays

Abstract

By improving resolution of home-made mutual-inductance measurements technique, a pronounced step-like structure (with the number of steps n = 4 for all AC fields) has been observed in the temperature dependence of AC susceptibility in artificially prepared two-dimensional Josephson Junction Arrays (2D-JJA) of unshunted N b − AlOx − N b junctions with βL(4.2K) = 30. Using a single-plaquette approximation of the overdamped 2D-JJA model, we were able to successfully fit our data assuming that steps are related to the geometric properties of the plaquette. The number of steps n corresponds to the number of flux quanta that can be screened by the maximum critical current of the junctions. The steps are predicted to manifest themselves in arrays with the inductance related parameter βL(T ) matching a "quantization" condition βL(0) = 2π(n + 1). PACS: 74.25.Ha, 74.50.+r, 74.80.Bj 1. Introduction. Many unusual and still not completely understood magnetic properties of Josephson Junction Arrays (JJAs) continue to attract attention of both theoreticians and experimentalists alike (for recent reviews on the subject see, e.g. [1,2,3,4] and further references therein). In particular, among the numerous spectacular phenomena recently discussed and observed in JJAs we would like to mention the dynamic temperature reentrance of AC susceptibility [2] (closely related to paramagnetic Meissner effect [3]) and avalanche-like magnetic field behavior of magnetization [4,5] (closely related to self-organized criticality (SOC) [6,7]). More specifically, using highly sensitive SQUID magnetometer, magnetic field jumps in the magnetization curves associated with the entry and exit of avalanches of tens and hundreds of fluxons were clearly seen in SIS-type arrays [5]. Besides, it was shown that the probability distribution of these processes is in good agreement with the SOC theory [7]. An avalanche character of flux motion was observed at temperatures at which the size of the fluxons did not exceed the size of the cell, that is, for discrete vortices. On the other hand, using a similar technique, magnetic flux avalanches were not observed in SNS-type proximity arrays [8] despite a sufficiently high value of the inductance L related critical parameter β L = 2πLI C /Φ 0 needed to satisfy the observability conditions of SOC. Instead, the observed quasi-hydrodynamic flux motion in the array was explained by the considerable viscosity characterizing the vortex motion through the Josephson junctions.

Dynamical reentrance and geometry imposed quantization effects in Nb–AlOx–Nb Josephson junction arrays

“…An avalanche character of flux motion was observed at temperatures at which the size of the fluxons did not exceed the size of the cell, that is, for discrete vortices. On the other hand, using a similar technique, magnetic flux avalanches were not observed in SNS-type proximity arrays (Ishikaev et In this section we present experimental evidence for manifestation of novel geometric effects in magnetic response of high-quality ordered 2D-JJA (Sergeenkov and Araujo-Moreira 2004). By improving resolution of home-made mutual-inductance measurements technique described in the beginning of this article, a pronounced step-like structure (with the number of steps n = 4 for all AC fields) has been observed in the temperature dependence of AC susceptibility in artificially prepared two-dimensional…”

“…For this reason, granularity is a term specially related to HTS, where magnetic and transport properties of these materials are usually manifested by a twocomponent response. In this scenario, the first component represents the intragranular contribution, associated to the grains exhibiting ordinary superconducting properties, and the second one, which is originated from intergranular material, is associated to the weak-link structure, thus, to the Josephson junctions network (Clark 1968, Saxena et al 1974, Yu and Saxena 1975, Resnick et al 1981, Sergeenkov 2001, Sergeenkov 2006, Sergeenkov and Araujo-Moreira 2004, Sergeenkov et al 2007. For single-crystals and other nearly-perfect structures, granularity is a more subtle feature that can be envisaged as the result of a symmetry breaking.…”

Unusually strong coherent response from grain-boundary Josephson network in polycrystalline Pr x Y1 − x Ba2Cu3O7 − δ

“…To understand the observed behavior of ∆χ ′ (h), it is quite reasonable to assume that the low-field AC response in our samples is related to a Josephson network mediated intergranular contribution [22,23,24] with λ L being the London penetration depth and l the thickness of the insulating layer. Based on the above critical fields, the flux penetration scenario can be described as follows.…”

“…To describe the observed phenomenon, we assume that intergranular contribution χ ′ J (h) is related to AC field h ac (t) = h cos(ωt) induced modulation of the Josephson current I ij (t) = (2π/Φ 0 )J ij sin θ ij (t) (where J ij is the Josephson energy) circulating in a closed plaquette (cluster) with a random distribution over contact areas S ij . Each such cluster involves adjacent superconducting grains i = 1, 2, ...N and j = i + 1 with an effective phase difference θ ij (t) = 2πS ij h ac (t)/Φ 0 across intergranular barriers [9,23,24,25,26]. In turn, due to the Ampere's law, this circulating current I ij (t) produces a net magnetic moment [25,26] µ(t) = ij I ij (t)S ij , leading us to H(t) = ij H ij (t) for the total Hamiltonian describing the flux dynamics of a single plaquette with…”

Polarization effects induced by a magnetic field in intrinsically granular superconductors

“…Both granular superconductors and artificially prepared arrays of Josephson junctions (JJAs) proved useful in studying the numerous quantum (charging) effects in these interesting systems, including blockade of Cooper pair tunneling [1], Bloch oscillations [2], propagation of quantum ballistic vortices [3], spin-tunneling related effects using specially designed SF S-type junctions [4,5], novel Coulomb effects in SIN IS-type nanoscale junctions [6], and recently observed geometric quantization phenomena [7] (see, e.g., Ref. [8] for the recent review on charge and spin effects in mesoscopic 2D Josephson junctions).…”