Evidence for Thermally Activated Spontaneous Fluxoid Formation in Superconducting Thin-Film Rings

We have measured the dynamics of individual magnetic fluxoids entering and leaving photolithographically patterned thin film rings of the underdoped high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, using a variable sample temperature scanning SQUID microscope. These results can be qualitatively described using a model in which the fluxoid number changes by thermally activated nucleation of a Pearl vortex in, and transport of the Pearl vortex across, the rin...

We report on the first experimental verification of the Zurek-Kibble scenario in an isolated superconducting ring over a wide parameter range. The probability of creating a single flux quantum spontaneously during the fast normal-superconducting phase transition of a wide Nb loop clearly follows an allometric dependence on the quenching time $\tau_{Q}$, as one would expect if the transition took place as fast as causality permits. However, the observed Zurek-Kibble scaling ex...

We have measured the dynamics of individual magnetic fluxoids entering and leaving thin film, photolithographically patterned rings of underdoped high-temperature superconductor BSCCO using a variable sample temperature scanning SQUID microscope. These measurements can be understood within a phenomenological model in which the fluxoid number changes by thermal activation of a Pearl vortex in the ring wall. We place upper limits on the "vison" binding energy in these samples f...

Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields. Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform larg...

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek...

The authors report magnetic measurements of fluxoid transitions in mesoscopic, superconducting aluminum rings. The transitions are induced by applying a flux to the ring so that the induced supercurrent approaches the critical current. In a temperature range near $T_c$, only a single fluxoid enters or leaves at a time, leading to a final state above the ground state. Upon lowering the temperature, several fluxoids enter or leave at once, and the final state approaches the gro...

Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the...

In this paper we use spontaneous flux production in annular superconductors to shed light on the Kibble-Zurek scenario. In particular, we examine the effects of finite size and external fields, neither of which is directly amenable to the KZ analysis. Supported by 1D and 3D simulations, the properties of a superconducting ring are seen to be well represented by analytic Gaussian approximations which encode the KZ scales indirectly. Experimental results for annuli in the prese...

We report observations of spontaneous formation of magnetic flux lines during a rapid quench of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films through T$_{c}$. This effect is predicted according to the Kibble-Zurek mechanism of creation of topological defects of the order parameter during a symmetry-breaking phase transition. Our previous experiment, at a quench rate of 20K/sec, gave null results. In the present experiment, the quench rate was increased to \TEXTsymbol{>} 10$^{8}$ K/se...

We describe an experimental search for spontaneous formation of flux lines during a rapid quench of thin YBaCuO films through Tc. This effect is expected according to the Kibble-Zurek mechanism of a creation of topological defects of the order parameter during a symmetry breaking phase transition. Spontaneously formed vortices were previously observed in superfluid 3He, while a similar experiment in superfluid 4He gave negative results. Using a high Tc SQUID, we measured both...