Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

Abstract

We study I-V characteristics of periodic square Nb wire networks as a function of temperature in a transverse magnetic eld, with a focus on three llings 2/5, 1/2, and 0.618 that represent very di erent levels of incommensurability. For all three llings, a scaling behavior of I-V characteristics is found, suggesting a nite temperature continuous superconducting phase transition. The lowtemperature I-V characteristics are found to have an exponential form, indicative of the domain-wall excitations.PACS numbers: 74.60.Ge, 64.60.CnThe presence of a quenched symmetry-breaking eld is known to have important consequences on the ordering of low temperature phases in many physical systems. A striking example is the pinning of a two-dimensional (2D) vortex lattice by a periodic potential in a superconducting wire network. Without pinning, a 2D elastic vortex lattice in homogeneous superconducting thin lms would not have long-range translational order at anynite temperature 1] and cannot have long-range superconducting phase coherence even at T = 0. A periodic pinning potential, however, when it is commensurate to the vortex lattice, can induce a gap in the low-energy excitation spectrum 2] and create a new thermodynamic phase 3] of a pinned 2D solid with true long-range translational order, and with superconducting phase coherence 4]. In the presence of a high-order commensurate (or incommensurate) potential, the competition between the vortex-vortex interactions and the vortex-network interactions leads to a whole new class of problems 5{7]. For example, the vortex lattice may: (a) become a 2D \ oating" solid and again lose its translational order and superconducting phase coherence at any temperature 5]; (b) form a metastable \glassy" phase 6]; (c) be pinned in a commensurate phase 7] and thus superconducting at low temperatures. The issue is far from being settled.Closely related to the low-temperature thermodynamic phase, the nature of the superconducting transition of a superconducting network in a magnetic eld is also not well understood. At lling f = 1=2, where f is the fraction of a ux quantum 0 = hc=2e per plaquette, for example, the vortex con guration of the ground state of the system has a checker-board pattern 4]. Thus, the ground state of the system has the discrete symmetry of the two-fold degeneracy as well as the continuous symmetry of an arbitrary global phase change. Two types of excitations are possible: vortex-antivortex pairs of the continuous phase variable and domain walls of the two ground states. If the two types of excitations do not interact, they should lead to two independent transitions 9]: a Kosterlitz-Thouless (KT) transition 8] in the underlying network and an Ising melting transition in the vortex lattice. The superconducting transition will be determined by the one with the lower transition-temperature. Interesting physics arises when the two types of excitations do couple 10]. Due to the screening of the vortex interactions by the domain walls, when the domain wall energy goes to zero ...

Zero-temperature transition and correlation-length exponent of the frustratedXYmodel on a honeycomb lattice

“…8,9 In superconducting systems with pinning described by XY models, frustration can be introduced by applying an external magnetic field as in periodic arrays of Josephson junctions, [10][11][12] superconducting wire networks, [13][14][15] and superconducting thin films with a periodic pattern of nanoholes. 16 The frustration parameter f sets the average density of vortices in the lattice of pinning centers and can be tuned by varying the strength of the external field.…”

Magnetic-flux periodic response of nanoperforated ultrathin superconducting films

“…Nonlinearities associated with the phase transition to the zero resistance state, which are expected at lower temperatures and have been observed in some wire arrays do not appear in this experiment's range [27,28,29]. The normal state resistances, R N , of neighboring film regions were compared to assess film homogeneity and found to agree to < 7%.…”

Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

“…Many of these effects show up as variations in the properties of the finite-temperature superconducting phase transitions at different fields. Recent and ongoing experiments have measured the critical exponents in superconducting arrays [3], opening the opportunity to do careful comparison of theory and experiment. In this Letter we examine the critical properties of the 2D XY model for two different values of the magnetic field in the densely frustrated regime (f ≫ 0) and in the presence of disorder.…”

“…64.70.Rh, 05.70.Fh, 64.60.Fr, 74.50.+r The frustrated XY model provides a convenient framework to study a variety of fascinating phenomena displayed by numerous physical systems. One experimental realization of this model is in two-dimensional arrays of Josephson junctions and superconducting wire networks [1][2][3]. A perpendicular magnetic field induces a finite density of circulating supercurrents, or vortices, within the array.…”

“…One experimental realization of this model is in two-dimensional arrays of Josephson junctions and superconducting wire networks [1][2][3]. A perpendicular magnetic field induces a finite density of circulating supercurrents, or vortices, within the array.…”