Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets

Abstract

We report a study of overdamped Josephson junction arrays with the geometry of periodically repeated Sierpinski gaskets. These model superconductors share essential geometrical features with truly random (percolative) systems. When exposed to a perpendicular magnetic field B, their euclidian or fractal behavior depends on the relation between the intervortex distance (imposed by B) and the size of a constituent gasket, and was explored with high-resolution measurements of the sample magnetoinductance L(B). In terms of the frustration parameter f expressing (in units of the superconducting flux quantum) the magnetic flux threading an elementary triangular cell of a gasket, the crossover between the two regimes occurs at fcN = 1/(2 × 4 N ), where N is the gasket order. In the fractal regime (f > fcN ) a sequence of equally spaced structures corresponding to the set of states with unit cells not larger than a single gasket is observed at multiples of fcN , as predicted by theory. The fine structure of L(f ) radically changes in the euclidian regime (f < fcN ), where it is determined by the commensurability of the vortex lattice with the effective potential created by the array. Anomalies observed in both the periodicity and the symmetry of L(f ) are attributed to the effect of a hidden incommensurability, which arises from the deformation of the magnetic field distribution caused by the asymmetric diamagnetic response of the superconducting islands forming the arrays.

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

“…It is also worth mentioning the recently observed geometric quantization (Sergeenkov and Araujo-Moreira 2004) and flux induced oscillations of heat capacity (Bourgeois et al 2005) in artificially prepared JJAs as well as recently predicted flux driven temperature oscillations of thermal expansion coefficient (Sergeenkov et al 2007) both in JJs and JJAs. At the same time, successful adaptation of the so-called two-coil mutual-inductance technique to impedance measurements in JJAs provided a high-precision tool for investigation of the numerous magnetoinductance (MI) related effects in Josephson networks (Martinoli and Leeman 2000, Meyer et al 2002, Korshunov 2003, Tesei et al 2006. To give just a few recent examples, suffice it to mention the MI measurements (Meyer et al 2002) on periodically repeated Sierpinski gaskets which have clearly demonstrated the appearance of fractal and Euclidean regimes for non-integer values of the frustration parameter, and theoretical predictions (Korshunov 2003) regarding a field-dependent correction to the sheet inductance of the proximity JJA with frozen vortex diffusion.…”

“…At the same time, successful adaptation of the so-called two-coil mutual-inductance technique to impedance measurements in JJAs provided a high-precision tool for investigation of the numerous magnetoinductance (MI) related effects in Josephson networks (Martinoli and Leeman 2000, Meyer et al 2002, Korshunov 2003, Tesei et al 2006. To give just a few recent examples, suffice it to mention the MI measurements (Meyer et al 2002) on periodically repeated Sierpinski gaskets which have clearly demonstrated the appearance of fractal and Euclidean regimes for non-integer values of the frustration parameter, and theoretical predictions (Korshunov 2003) regarding a field-dependent correction to the sheet inductance of the proximity JJA with frozen vortex diffusion. Besides, recently (Tesei et al 2006) AC magnetoimpedance measurements performed on proximity-effect coupled JJA on a dice lattice revealed unconventional behaviour resulting from the interplay between the frustration f created by the applied magnetic field and the particular geometry of the system.…”

Manifestation of geometric resonance in current dependence of AC susceptibility for unshunted array of Nb–Alx–Nb Josephson junctions

“…Furthermore, a careful analysis of Eq. (2) reveals that the observed resonance occurs for x ffi x r ðIÞ, where x = 40 kHz is the frequency of the applied AC current I AC ðtÞ ¼ I sin xt and x r ðIÞ ¼ 2 p À Á xLxI U 0 is the current induced resonance frequency with L x ¼ L 1þx 2 s 2 being the dynamical inductance of the plaquette [2,17,18].…”

A driven fractal network: Possible route to efficient thermoelectric application

“…These localized states become delocalized in the presence of a magnetic field 3 . Owing to such distinctive properties, SPG structures have been studied extensively over the years in many contexts, and several other unique features have been observed [4][5][6][7][8][9][10][11][12] .…”