We calculate the modification of the local electronic structure caused by a single local impurity on the surface of a 3D Topological Insulator. We find that the LDOS around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state(s) -however, this is not sufficient to (locally) destroy the Dirac point. We also calculate the non-trivial spin textures created near the magnetic impurities and discover anisotropic RKKY coupling between them. PACS numbers: 72.25.Dc, 75.30.Hx,d * Electronic address: rrbiswas@physics.harvard.edu † Electronic address: avb@lanl.gov 1 A. V. Balatsky, I. Vekhter, and J.-X. Zhu, Rev. Mod. Phys. 78, 373 (2006).

In this Letter we present detailed study of the density of states near defects in Bi2Se3. In particular, we present data on the commonly found triangular defects in this system. While we do not find any measurable quasiparticle scattering interference effects, we do find localized resonances, which can be well fitted by theory [R. R. Biswas and A. V. Balatsky, Phys. Rev. B 81, 233405(R) (2010)] once the potential is taken to be extended to properly account for the observed defects. The data together with the fits confirm that while the local density of states around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state, the Dirac point is not locally destroyed. We discuss our results in terms of the expected protected surface state of topological insulators.

Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry. However, the overwhelming majority of studies demonstrate the presence of a finite density of states near the Dirac point even once topological insulators become magnetic. Here, we map the response of topological states to magnetic impurities at the atomic scale. We demonstrate that magnetic order and gapless states can coexist. We show how this is the result of the delicate balance between two opposite trends, that is, gap opening and emergence of a Dirac node impurity band, both induced by the magnetic dopants. Our results evidence a more intricate and rich scenario with respect to the once generally assumed, showing how different electronic and magnetic states may be generated and controlled in this fascinating class of materials.