Magnetic-flux quanta in superconducting thin films observed by electron holography and digital phase analysis

Singly quantized magnetic fluxes in superconducting lead films have been directly observed in the form of magnetic-flux-line distributions by using an electron-holography technique. Combining this with the digital-phase-analysis method, we were able to determine the flux quantum h/2e for individual fluxes with a precision of {~}h/100e, and analyze the distributions of field-vector components around the fluxon centers. The internal-field distributions obtained were compared with those calculated from the Ginzburg-Landau equations with use of some models, and an overall agreement was found between them. We also observed the changes of the magnetic-flux structures of lead thin films as a function of their thickness. Fluxon pairs were observed in 0.2-{μ}m-thick films, which may correspond to those suggested by Kosterlitz-Thouless theory.