Current induction and macroscopic forces for superconducting strings

Superconducting strings are topological defects appearing in cosmological early stage models, in tentative explanations of the high energy cosmic rays, galaxy formation and even in condensed matter to deal with some kind of superconductors. The main topic studied in this paper is the inverse photoelectric effect for superconducting lines namely, it is estimated the cross section corresponding to the adsorption of a fermion with the consequent emission of a photon. This issue is of importance, as some of these fermions can become a zero mode inside the core of the object, thus traveling at the speed of light and generating a possibly large current, whose cosmological implications has been discussed in a variety of works. A discussion is introduced comparing it to the Aharonov-Bohm cross section and relating them to the associated (Magnus) forces. It is also obtained a quite explicit description of the bound states and a version of Weyl’s law for the energies.

Figure 1

The initial and final configuration for a fermion incident over the string. For simplicity, only fermions incident transversally will be considered. The word “photon” should not be taken too literally, as is meant any type of Abelian gauge field.