Exchange-field-modulated 0-π transition and chiral edge supercurrents in a superconductor/ferromagnetic topological insulator/superconductor junction

We study theoretically the Josephson effect in an s-wave superconductor/two-dimensional (2D) ferromagnetic topological insulator (TI)/s-wave superconductor junction by the Matsubara Green's function method. It is found that the direction of the edge supercurrents through the Josephson junction can reverse (i.e., 0-pi transition occurs) when both the time-reversal symmetry and sublattice symmetry are broken by inducing the exchange field in the magnetically doped TI. The unconventional 0 and pi states are robust against the weak disorder, which is guaranteed by the topological properties of the quantum spin Hall state in the 2D ferromagnetic TI. Moreover, as the superconducting phase difference between the two superconductors is 0 or pi, the two edge supercurrents have equal magnitude but are in the opposite directions, so that the total supercurrents vanish and the chiral edge supercurrents emerge. The feasible experimental detection of the chiral edge supercurrents is indicated.