SUPERCONDUCTING WIRE NETWORK UNDER SPATIALLY MODULATED MAGNETIC FIELD

Abstract

The super/normal phase boundary of a two-dimensional (2D) superconducting wire network exhibits characteristic Little-Parks oscillation as a function of the magnetic frustration α (perpendicular magnetic flux piercing the unit cell). The fine structure of the Tc(H) curve reflects the edge of the so-called Hofstadter butterfly spectrum which represents the Bloch band of tight binding electrons on a corresponding 2D lattice under a perpendicular magnetic field. Thus the Tc(H) curve has local maxima at simple fractional values of α, which correspond to stable vortex configurations. In this work, we address the case in which superconducting network is subjected to both a spatially modulated magnetic field and a uniform magnetic field. We measured the dependence of the Tc(H) curve on the field modulation amplitude β (expressed in terms of flux per plaquette) and compared the results with the corresponding Hofstadter butterfly spectra calculated by the matrix diagonalization method. The nature of super/normal transition in 2D superconducting wire networks and Josephson junction arrays has been a subject of extensive studies. The transition at zero magnetic field is generally understood in terms of Kosterlitz-Thouless (KT) transition, the hallmark of which is a “universal jump” at T=TKT of the exponent in the power law current-voltage (I-V) characteristics. The super/normal transition in magnetic fields is governed by subtle competition between the vortex-vortex interactions and the interaction of a vortex with the pinning potentials both periodic and random. In particular, the overall interaction of the vortex system with the periodic potential should be sensitive to the value of α. Various models of phase transitions including, melting and floating of a vortex solid, vortex glass (VG) phase transition, and formation commensurate domains have been theoretically proposed and experimentally pursued. However, there still remain ambiguities in the comparison of the experimental data and theoretical models, so that the nature of superconducting transition in networks has so far been elusive. In order to shed light on the issue, we conducted I-V characteristics measurement in the present system with spatially varying magnetic field which is different from the usually studied case of uniform applied field.