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Magnetism-induced massive Dirac spectra and topological defects in the surface state of Cr-doped Bi$_2$Se$_3$-bilayer topological insulators

Proximity-induced magnetic effects on the surface Dirac spectra of topological insulators are investigated by scanning tunneling spectroscopic (STS) studies of bilayer structures consisting of undoped Bi2Se3 thin films on top of Cr-doped Bi2Se3 layers. For thickness of the top Bi2Se3 layer equal to or smaller than 3 quintuple layers (QL), a spatially inhomogeneous surface spectral gap Δopens up below T_c^{2D}, which is much higher than the bulk Curie temperature T_c^{3D}. The mean value and spatial homogeneity of the gap Δgenerally increase with increasing c-axis magnetic field (H) and increasing Cr doping level (x), suggesting that the physical origin of this surface gap is associated with proximity-induced c-axis ferromagnetism. On the other hand, the temperature (T) dependence of Δis non-monotonic, showing an initial increase below T_c^{2D} followed by a dip and then reaching maximum at T << T_c^{3D}. These phenomena may be attributed to proximity magnetism induced by two types of contributions with different temperature dependence: a 3D contribution from the bulk magnetism that dominates at low T, and a 2D contribution associated with the RKKY interactions mediated by surface Dirac fermions, which dominates at T_c^{3D} << T < T_c^{2D}. Additionally, spatially localized sharp resonant spectra are found along the boundaries of gapped and gapless regions. These spectral resonances are long-lived at H = 0 and become suppressed under strong c-axis magnetic fields, and are attributed to magnetic impurity-induced topological defects in the spin texture of surface Dirac fermions.