  Fermions localized within vortex cores can form one-dimensional Fermi
liquids. The nonzero density of states in these Fermi-liquids can lead to
instability of the symmetric structure of the vortex core. We consider a
symmetry breaking which is obtained due to spontaneous admixture of the
spin-triplet p-wave component of the order parameter in conventional s-wave
vortex in the presence of magnetic field. This occurs at low enough temperature
and leads to an asymmetric shape of the vortex core. Similar phenomenon of the
symmetry breaking induced by the core fermions occurs in electroweak
$Z$-strings (S.G. Naculich, Phys. Rev. Lett., 75 (1995), 998).
