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 energiesThe present work is supported by CONICET, Argentina and by the Grant PICT 2020-02181. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant agreement No. 777822. F. C. is partially supported by the PID2020–113350 GB-I00 grant of the MICINN (Spain) and by “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S