Topological strings and fractional pumping in superconductors

Quantum flux vortices are topological line defects of the pairing order parameter in a superconductor in three dimensions. On the other hand, chiral gapless Majorana fermions live along another kind of topological line defects that involve non-trivial spatial modulations of the Bogoliubov-de Gennes Hamiltonian. Topological strings are combinations of these two types of line defects. I theoretically describe the different fractional pumping processes through linking topological strings in superconducting Dirac semimetals.