Bridge in micron-sized Bi2Sr2CaCu2O8+y sample act as converging lens for vortices

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Abstract

We report on direct imaging of vortex matter nucleated in micron-sized Bi2Sr2CaCu2O8+y superconducting samples that incidentally present a bridge structure. We find that when nucleating vortices in a field-cooling condition the deck of the bridge acts as a converging lens for vortices. By means of Bitter decoration images allowing us to quantify the enhancement of vortex-vortex interaction energy per unit length in the deck of the bridge, we are able to estimate that the deck is thinner than 0.6 μm. We show that the structural properties of vortex matter nucleated in micron-sized thin samples are not significantly affected by sample-thickness variations of the order of half a micron, an important information for type-II superconductors-based mesoscopic technological devices.

Introduction

The miniaturization of technological devices have driven the study on how the confinement and surface effects alter the physical properties of systems of interacting objects [1], [2], [3], [4], [5]. Nucleating small crystals of vortex matter in micron-sized superconducting samples gives us the possibility of studying this general problem in a playground where the relevant parameters are easily controlled. Indeed, the density of interacting objects can be tuned by applied field, the interaction of vortices with the underlying disorder of the host sample can be altered by changing temperature, and the confinement and surface effects can be tailored by a suitable design of the samples [6], [7], [8], [9], [10], [11]. There is sufficient evidence in the literature that size and surface effects in micron-sized superconducting samples produce dramatic changes on their physical properties. For instance, for type-I superconductors of one-micron or sub-micron size, the boundary conditions imposed by the shape and geometry of the sample to the quantization of angular momentum of the Cooper pair wave function govern the superconducting phase boundary, and stabilizes a complex phase diagram with several confinement-induced transitions [6], [7]. In the case of micron-sized type-II superconductors, changing the applied field induces not only different regimes in the magnetic response of the system, but can also trigger a structural transition in vortex matter from a giant vortex state with multiple flux quanta to a glass state with single-fluxoid vortices [8], [9].

On increasing the sample size to tens of microns, and then nucleating crystals with few hundred vortices, some works report on how the thermodynamic, magnetic, and structural properties of vortex matter are significantly different from the bulk case [5], [10], [11], [12], [13], [14], [15], [16]. These works warn on a need of better characterizing these properties for potential applications of these systems to miniaturized superconducting devices. Regarding the structural properties, a proliferation of topological defects induced by confinement has been reported for crystals with few hundred vortices in the case of the layered Bi2Sr2CaCu2O8+y system [14], [16]. For thin micron-sized disks, topological defects in the vortex structure proliferate on decreasing the radius from 50 to 30 μm and also present an inhomogeneous spatial distribution [16]. At the vicinity of the edge, the number of defects amplifies over a characteristic length in which vortex rows tend to bend mimicking the shape of the sample. In contrast, within the center of the samples the positional order of the vortex structure is consistent with the Bragg-glass phase. This healing length at which topological defects are cured towards the center may be a key quantity to model confinement effects in vortex matter nucleated in micron-sized samples. The geometry of samples is also another parameter that affects the structural properties of vortex crystals at the mesoscopic scale. For example, a smaller density of topological defects is nucleated in square than disk thin mesoscopic samples of the same typical size. In addition, in the former case the vortex rows accommodate parallel to the edges without bending [14].

Previous studies have reported data in samples with a constant thickness, then very little is known about the effect of varying the sample thickness in micron-sized samples. In order to amplify the effect of sample thickness variations, it is desirable to choose a superconducting material with large line energy per unit length, εL=(Φ0/4πλ)2lnκ. A material such as Bi2Sr2CaCu2O8+y, with κ200, seems a suitable candidate for studying this issue. Vortex matter in bulk samples of this material presents a rich phase diagram that includes liquid and glassy phases with different magnetic [17], [18], [19], [20], [21] and structural properties [22], [23], [24], [25] depending on the type of disorder of the host sample. In this paper we study the structural properties of vortex matter in micron-sized thickness-modulated samples of the extremely-anisotropic pristine Bi2Sr2CaCu2O8+y superconductor. We directly image the 700-vortices crystal nucleated in a square thin sample of roughly 40 μm side and 2 μm thickness that incidentally presents a bridge structure. We find that when nucleating vortices in a field-cooling condition the deck of the bridge acts as a converging lens for vortices. Irrespective of the higher vortex density in the bridge than in the base, the structural properties of vortex matter in both regions are not significantly dissimilar. By means of energetic arguments we estimate that the deck of the bridge is 0.6μm thick or even thinner. This quantitative estimation allows us to measure a top limit on how thin can be the samples in order for the structure of vortex crystals in mesoscopic thin samples not being significantly affected by sample-thickness variations and still behaving as a three-dimensional structure.

Section snippets

Method

The micron-sized square thin sample with a bridge structure was engineered from a bulk, pristine, and optimally-doped Bi2Sr2CaCu2O8+y crystal with a critical temperature Tc=90 K. The sample was obtained following a top-down procedure that combines optical lithography with physical ion-milling, see Refs. [5], [11] for further technical details. With the aim of directly imaging the vortex structure nucleated in such samples, we cleave the physically-etched bulk crystal, then manipulate one by one

Results

Fig. 1 shows a snapshot of the vortex structure nucleated in the micron-sized Bi2Sr2CaCu2O8+y square sample with a bridge structure, following a field-cooling process at an applied field of 12 Oe. The picture is obtained from a magnetic decoration performed at 4.2 K and vortices are observed as white dots in the SEM image of Fig. 1. The most notorious fact of this snapshot is that the bridge structure acts as a converging lens for the vortex structure: The average vortex density in the deck is

Discussion

The focusing effect occurs probably at the beginning of the field cooling process. Even though the decoration of vortex positions is performed at 4.2 K, in a field-cooling process this technique actually captures a snapshot of the vortex structure frozen at a temperature Tfreez close to the irreversibility line [23]. At the irreversibility temperature Tirr, weak bulk pinning sets in and then the vortex structure is frozen at lengthscales of the lattice spacing a. On further cooling, vortices

Conclusion

In conclusion, we have found that micron-sized samples of type-II superconductors presenting a bridge-like structure might be effective converging lens devices focusing vortex density in the deck of the sample. Here we reveal this effect in the case of a 700-vortices structure with a 11 G density nucleated in a mesoscopic thin Bi2Sr2CaCu2O8+y sample with 40 μm side, 2 μm nominal thickness, and presenting a bridge with a 0.6 μm-thick deck. We find that in this material with large line energy

Declaration of Competing Interest

I declare no conflict of interest.

Acknowledgments

This work was supported by the Argentinean National Science Foundation (ANPCyT) under Grant PICT 2017–2182; by the Universidad Nacional de Cuyo research grant 06/C566-2019; and by Graduate Research fellowships from IB-CNEA for J. P. and from CONICET for J.P., J. A. S., and N. R. C. B. We thank to I. Artola-Vinciguerra for assistance with SEM images, M. Li for growing the bulk single crystals from which the samples where generated, and to H. Pastoriza for support in the micro-engineering

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