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 ...

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The peak effect (PE) has been observed in a twinned crystal of YBa 2 Cu 3 O 7−δ for H c in the low field range, close to the zero field superconducting transition temperature (T c (0)) . A sharp depinning transition succeeds the peak temperature T p of the PE. The PE phenomenon broadens and its internal structure smoothens out as the field is increased or decreased beyond the interval between 250 Oe and 1000 Oe. Moreover, the PE could not be observed above 10 kOe and below 20 Oe. The locus of the T p (H) values shows a reentrant characteristic with a nose like feature located at T p (H)/T c (0)≈0.99 and H≈100 Oe (where the FLL constant a 0 ≈penetration depth λ). The upper part of the PE curve (0.5 kOe

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