Generic Current-Carrying Strings
  We investigate the standard model in a cosmic string background and show that the electroweak symmetry is partially restored. For a range of parameters the electroweak Higgs field can wind in this region, producing an electroweak string stabilised by the cosmic string background. In this case there are quark and lepton zero modes that result in the string becoming superconducting at the electroweak scale. If the electroweak Higgs field does not wind, there are no zero modes, but there are fermion bound states. These bound states can also carry a current. 
Anne-Christine Davis, Warren B. Perkins