Fractional vortices on grain boundaries --- the case for broken time   reversal symmetry in high temperature superconductors
  We discuss the problem of broken time reversal symmetry near grain boundaries in a d-wave superconductor based on a Ginzburg-Landau theory. It is shown that such a state can lead to fractional vortices on the grain boundary. Both analytical and numerical results show the structure of this type of state. 
D. Bailey, M. Sigrist, and R. B. Laughlin