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(Color online) (a)-(c) Band structures of topological insulator thin films. (a) M = 0 and Δ = 0 and (b) M = 0 and Δ ≠ 0, which correspond to the larger and smaller thickness of pristine thin films, respectively. (c) M ≠ 0 and Δ ≠ 0, which corresponds to the smaller thickness of thin films with ferromagnetic order. (d) Phase diagram of Hall conductance as a function of Δ and M.
(Color online) The calculated magnetic moments of X-doped TlBiTe2 (TlBiSe2), where X = Ti, Cr, and Fe. The slashed area indicates the insulating magnetic states. Inset is the difference of formation energies between X@Bi and X@Fe, ΔEF = EX@Bi−EX@Tl, in X-doped TlBiTe2 (TlBiSe2). The substitutional Au cannot induce magnetism and not shown here.
(Color online) TDOS and partial DOS of X-doped TlBiTe2 with X at Bi [(a)-(d)] and Tl [(e)-(h)] sites, where X = Cr, Fe, Ti, and Au. The Fermi level is indicated by the dashed line at 0 eV.
Values of Cr-Cr (Fe-Fe) distance d and magnetization energy Emag for the ground state of the two-atom-doped TlBiTe2 and TlBiSe2, which have the insulating magnetic states, with Cr@Bi, Cr@Bi, and Fe@Bi.
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