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Register a new userImaging Flux Vortices in Type II Superconductors with a Commercial Transmission Electron Microscope
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Flux vortices in superconductors can be imaged using transmission electron microscopy because the electron beam is deflected by the magnetic flux associated with the vortices. This technique has a better spatial and temporal resolution than many other imaging techniques and is sensitive to the magnetic flux density within each vortex not simply the fields at the sample surface. Despite these advantages, only two groups have successfully employed the technique using specially adapted instruments. Here we demonstrate that vortices can be imaged with a modern, commercial transmission electron microscope operating at 300 kV equipped with a field emission gun, Lorentz lens and a liquid helium cooled sample holder. We introduce superconductivity for non-specialists and discuss techniques for simulating and optimising images of flux vortices. Sample preparation is discussed in detail as the requirement for samples with very large (>10um), flat areas so that the image is not dominated by diffraction contrast is the main difficulty with the technique. We have imaged vortices in superconducting Bi2Sr2CaCu2O8+d and use correlation functions to investigate the ordered arrangements they adopt as a function of applied magnetic field.
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We report the successful imaging of flux vortices in single crystal MgB2 using transmission electron microscopy. The specimen was thinned to electron transparency (350 nm thickness) by focussed ion beam milling. An artefact of the thinning process was the production of longitudinal thickness undulations of height 1-2 nm in the sample which acted as pinning sites due to the energy required for the vortices to cross them. These had a profound effect on the patterns of vortex order observed which we examine here. Supplementary information can be downloaded from http://www-hrem.msm.cam.ac.uk/people/loudon/#publications
Imaging of flux vortices in high quality MgB$_2$ single crystals has been successfully performed in a commercial Field Emission Gun-based Transmission Electron Microscope. In Cryo-Lorentz Microscopy, the sample quality and the vortex lattice can be monitored simultaneously, allowing one to relate microscopically the surface quality and the vortex dynamics. Such a vortex motion ultimately determines the flow resistivity, $rho_{f}$, the knowledge of which is indispensable for practical applications such as superconducting magnets or wires for Magnetic Resonance Imaging. The observed patterns have been analyzed and compared with other studies by Cryo-Lorentz Microscopy or Bitter decoration. We find that the vortex lattice arrangement depends strongly on the surface quality obtained during the specimen preparation, and tends to form an hexagonal Abrikosov lattice at a relatively low magnetic field. Stripes or gossamer-like patterns, recently suggested as potential signatures of an unconventional behavior of MgB$_2$, were not observed.
We analyze the structure of an $s-$wave superconducting gap in systems with electron-phonon attraction and electron-electron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap, $Delta (omega_m)$, necessarily changes sign along the Matsubara axis. We analyze the sign-changing gap function from a topological perspective using the knowledge that a nodal point of $Delta (omega_m)$ is the center of dynamical vortex. We consider two models with different cutoffs for the repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane upon changing the relative strength of the attractive and repulsive parts of the interaction. We discuss how the presence of dynamical vortices affects the gap structure along the real axis, detectable in ARPES experiments.
We consider the current density distribution function of a flux creep regime in type-II superconductors by mapping the flux creep process to the dynamics of a model with a self-organized criticality. We use an extremal Robin Hood type model which evolves to Beens type critical state to treat magnetic flux penetration into a superconductor and derive an analog of the current-voltage characteristics in the flux creep region.
Images of flux vortices in superconductors acquired by transmission electron microscopy should allow a quantitative determination of their magnetic structure but so far, only visual comparisons have been made between experimental images and simulations. Here, we make a quantitative comparison between Fresnel images and simulations based on the modified London equation to investigate the magnetic structure of flux vortices in MgB2. This technique gives an absolute, low-field (~30 Oe) measurement of the penetration depth from images of single vortices. We found that these simulations gave a good fit to the experimental images and that if all the other parameters in the fit were known, the penetration depth for individual vortices could be measured with an accuracy of +/- 5 nm. Averaging over 17 vortices gave a penetration depth in the ab plane of 113 +/- 2 at 10.8 K assuming that the entire thickness of the sample was superconducting. The main uncertainty in this measurement was the proportion of the specimen which was superconducting. Allowing for a non-superconducting layer of up to 50 nm thickness on the specimen surfaces gave a penetration depth in the range 100-115 nm, close to values of 90 +/- 2 nm obtained by small-angle neutron scattering and 118-138 nm obtained by radio-frequency measurements. We also discuss the use of the transport of intensity equation which should, in principle, give a model-independent measure of the magnetic structure of flux vortices.
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