Stability of an electroweak string with a fermion condensate
  A solution of the standard electroweak theory with a single lepton family is constructed, consisting of a cosmic string and a fermion condensate within its core. The stability of this system to small perturbations is examined, and it is found that stability is not enhanced relative to the bare electroweak string. The presence of quark zero modes is shown to violate the existence criteria for embedded defects. 
Michael A. Earnshaw, Warren B. Perkins