FIG. 2: The calculated density of states (DOS) for Bi$_{2}$Se$_{3}$ doped with different transi- tion metal elements . The Fermi level is located at energy zero, and the positive and negative values of DOS are used for up and down spin, respectively. The blue lines are projected partial DOS of the 3 d states of transition metal ions. It is shown that Cr or Fe doping will give the insulating magnetic state. 16 -40 -20  0  20  40 -4 -3 -2 -1  0  1 DOS (states/eV)  Energy (eV) (a) Ti total 3d -40 -20  0  20  40 -4 -3 -2 -1  0  1 DOS (states/eV)  Energy (eV) (b) V total 3d -40 -20  0  20  40 -4 -3 -2 -1  0  1 DOS (states/eV)  Energy (eV) (c) Cr total 3d -40 -20  0  20  40 -4 -3 -2 -1  0  1 DOS (states/eV)  Energy (eV) (d) Fe total 3d