Observation of individual vortices trapped along columnar defects in high-temperature superconductors

Tonomura, Akira; Kasai, H.; Kamimura, O.; Matsuda, Tsuyoshi; Harada, Ken; Nakayama, Yasuo; Shimoyama, J.; Kishio, K.; Hanaguri, T.; Kitazawa, K.; Sasase, Masato; Okayasu, Satoru

doi:10.1038/35088021

Cited by 132 publications

(89 citation statements)

References 14 publications

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“…Some of these effects have been studied theoretically, using analytic 18 and numerical 19 methods. Bulk HTSC samples with periodic arrays of columnar pins have not been fabricated yet, but the technology for doing this appears to be within reach 20 .…”

Section: Introductionmentioning

confidence: 99%

Vortices in layered superconductors with columnar pins: A density-functional study

Dasgupta

Valls²

2002

Phys. Rev. B

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We use numerical minimization of a model free energy functional to study the effects of columnar pinning centers on the structure and thermodynamics of a system of pancake vortices in the mixed phase of highly anisotropic layered superconductors. The magnetic field and the columnar pins are assumed to be perpendicular to the layers. Our methods allow us to study in detail the density distribution of vortices in real space. We present results for the dependence of the average number of vortices trapped at a pinning center on temperature and pinning strength, and for the effective interaction between nearby pinned vortices arising from short-range correlations in the vortex liquid. For a commensurate, periodic array of pinning centers, we find a line of first order vortex lattice melting transitions in the temperature T vs. pin concentration c plane, which terminates at an experimentally accessible critical point as c is increased. Beyond this point, the transition is replaced by a crossover. Our results should also apply, with little change, to thin-film superconductors with strong point pinning.

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Section: Introductionmentioning

confidence: 99%

Vortices in layered superconductors with columnar pins: A density-functional study

Dasgupta

Valls²

2002

Phys. Rev. B

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“…Among the remaining problems, is the shape of a vortex/flux line and the study of its time evolution. The observation of inclined flux lines in superconductors was only possible due to recent advances in electron microscopy [10]. In gaseous BEC, one has comparably easy access to the vortex line because the density of the atom cloud is low.…”

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confidence: 99%

Dynamics of a Single Vortex Line in a Bose-Einstein Condensate

2002

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We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 seconds. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.PACS numbers: 03.75. Fi,32.80.Pj,67.40.Vs The macroscopic motions of quantum and classical fluids are dramatically different. The description of a quantum fluid by a macroscopic wave function ψ = √ ρ e iθ imposes strong constraints upon its velocity field. At a position of non-vanishing density ρ, the velocity is related to the phase θ by v = ∇θ/m, where m is the mass of a particle of the fluid. Hence ∇ × v = 0. A rotational motion of the fluid can be obtained only through the nucleation of vortex lines, along which the density is zero and around which the circulation of the velocity is quantized in units of h/m [1, 2].Quantized vortices play an essential role in the dynamics of all quantum macroscopic objects. Examples are flux lines in superconductors [3], and vortex lines in superfluid liquid helium [4] and gaseous Bose-Einstein condensates (BEC) [5,6,7,8,9]. Among the remaining problems, is the shape of a vortex/flux line and the study of its time evolution. The observation of inclined flux lines in superconductors was only possible due to recent advances in electron microscopy [10]. In gaseous BEC, one has comparably easy access to the vortex line because the density of the atom cloud is low. A few disordered vortex lines have been observed by taking tomographic images perpendicular to the long axis of a cigar shaped condensate [7]. An array of many vortex lines in a pancake shaped condensate has been observed by transverse imaging of the whole atom cloud [11].In this Letter we report the full length observation of a single vortex line in a cigar shaped condensate. We find that as a result of spontaneous symmetry breaking the line is generally bent. Our experimental results confirm recent predictions, in which the shape of the vortex line minimizing the energy of the gas was derived for a given rotation frequency [12,13,14,15,16]. We also study the time evolution of the shape of the line. As the angular momentum of the gas slowly decays, the bending of the vortex line and its deviation from to the center of the trap increase. We investigate the influence of temperature on these dynamics. From our results one can hope to draw some indications for the shape and dynamics of the vortex/flux line in systems where a direct observation is not yet possible.Our 87 Rb condensate is formed by radio-frequency (rf) evaporation of 10 9 atoms in a Ioffe-Pritchard magnetic trap. The atoms are spin-polarized in the F = m F = 2 state. The magnetic trap has a longi...

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“…We use low-temperature scanning electron microscopy (LTSEM) [2,3,4,5] to image vortices in dc SQUID washers [6,7]. Most techniques for vortex imaging, such as Lorentz microscopy [8], scanning SQUID microscopy [9,10], scanning Hall microscopy [11] or magneto-optics[12] rely on the detection of the stray magnetic field produced in close proximity to a vortex. In contrast, vortex imaging by LTSEM is different from those techniques, as it is based on the electron-beaminduced apparent displacement of a vortex, pinned at position r in the (x, y)-plane of a SQUID washer, which is detected as a change of stray magnetic flux Φ(r) coupled to the SQUID.…”

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Sheet-current distribution in a dc SQUID washer probed by vortices

et al. 2006

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We present a novel method, based on vortex imaging by low-temperature scanning electron microscopy (LTSEM), to directly image the sheet-current distribution in YBa2Cu3O7 dc SQUID washers. We show that the LTSEM vortex signals are simply related to the scalar stream function describing the vortex-free circulating sheet-current distribution J . Unlike previous inversion methods that infer the current distribution from the measured magnetic field, our method uses pinned vortices as local detectors for J . Our experimental results are in very good agreement with numerical calculations of J .PACS numbers: 68.37. Hk, 74.25.Op, 85.25.Dq Spatially resolved techniques can provide important insight into current flow, arrangement of vortices, flux pinning, and noise in superconductors and their mutual interactions. So far there has been only one method of imaging the current distribution in superconductors: The magnetic field distribution on top of a superconducting thin film is measured, e.g. by magneto-optics, from which the current distribution can then be calculated by inverting the Biot-Savart law [1].In this paper we present a novel method to directly image the sheet-current distribution in a YBa 2 Cu 3 O 7 thin film. We use low-temperature scanning electron microscopy (LTSEM) [2,3,4,5] to image vortices in dc SQUID washers [6,7]. Most techniques for vortex imaging, such as Lorentz microscopy [8], scanning SQUID microscopy [9,10], scanning Hall microscopy [11] or magneto-optics[12] rely on the detection of the stray magnetic field produced in close proximity to a vortex. In contrast, vortex imaging by LTSEM is different from those techniques, as it is based on the electron-beaminduced apparent displacement of a vortex, pinned at position r in the (x, y)-plane of a SQUID washer, which is detected as a change of stray magnetic flux Φ(r) coupled to the SQUID. Hence, the contrast of the LTSEM vortex signals directly senses ∇Φ(r). Recently, Clem and Brandt [13] have shown that Φ(r) is proportional to the scalar stream function G(r) that describes the circulating sheet-current density J(r) flowing in the vortex-free case at position r in the SQUID washer. In this paper we show that this relationship allows us to use the vortices as local detectors for J(r): At each position a vortex has been imaged, we can directly determine J(r) without complicated calculations.In our experiments, we investigated several dc SQUID washers [see Fig. 1(a)] fabricated from epitaxially grown d=80 nm thick c-axis oriented YBa 2 Cu 3 O 7 (YBCO) thin * Electronic address: koelle@uni-tuebingen.de films. We will present an analysis of LTSEM data obtained from one representative device with washer size 120 µm × 305 µm, with a 100 µm long and 4 µm wide slit. The 1 µm wide Josephson junctions are formed by a 24 • symmetric grain boundary in the underlying SrTiO 3 substrate. For imaging by LTSEM, the YBCO SQUIDs are mounted on a magnetically shielded, liquid nitrogen cooled cryostage of an SEM [14] and read out by a standard flux-locked loop (FLL) w...

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Observation of individual vortices trapped along columnar defects in high-temperature superconductors

Cited by 132 publications

References 14 publications

Vortices in layered superconductors with columnar pins: A density-functional study

Vortices in layered superconductors with columnar pins: A density-functional study

Dynamics of a Single Vortex Line in a Bose-Einstein Condensate

Sheet-current distribution in a dc SQUID washer probed by vortices

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