On the interpretation of Lorentz and holographic interference images of superconducting fluxons:

Imaging flux vortices in type II superconductors with a commercial transmission electron microscope

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 300kV 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 main difficulty with the technique is the requirement for samples with very large (>10microm), flat areas so that the image is not dominated by diffraction contrast. We have imaged vortices in superconducting Bi(2)Sr(2)CaCu(2)O(8-delta) and use correlation functions to investigate the ordered arrangements they adopt as a function of applied magnetic field.

On the calculation of the phase shift of superconducting fluxons: from the isolated to the lattice case

The numerical problems associated to the calculation of the phase shift due to a flux line lattice (FLL) in a thin superconducting specimen are presented and discussed. In order to be able to adequately treat the periodic case, the Fourier transform of the phase shift due to a flux tube is needed. This result is obtained by means of a new approach, where the phase shift is calculated from the beginning in the reciprocal space, treating separately each Fourier coefficient of the magnetic vector potential. The equivalence with the old approach is demonstrated and the utility of the new formulation for calculating the phase shift of closely packed FLL shown.