Calculation of tunnel current due to vortex core excitations in clean superconductors

The conductance associated with low lying vortex core excitations in a clean superconducting tunnel junction containing well separated flux vortices whose axes are perpendicular to the insulating barrier is calculated. The method combines the Bardeen tunnelling matrix element with the Caroli-Bardeen description of clean limit vortices. Account is taken of the anisotropy of the density of states and of the angular selectivity of the barrier as a function of its thickness and band gap. For a typical case the tunnel conductance between a vortex and a normal metal (VIM) is around one third of that predicted by inserting the vortex density of states directly into conventional tunnelling formulae. However, in tunnelling transitions between two vortices (VIV) there is also an angular momentum conservation rule which results in almost zero conductance at low bias.