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We calculate exact zero-temperature real space properties of a substitutionalmagnetic impurity coupled to the edge of a zigzag silicene-like nanoribbon.Using a Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] and the densitymatrix renormalization group method, we obtain a realistic description ofstanene and germanene that includes the bulk and the edges as boundaryone-dimensional helical metallic states. Our results for substitutionalimpurities indicate that the development of a Kondo state and the structure ofthe spin correlations between the impurity and the electron spins in themetallic edge state depend considerably on the location of the impurity. Morespecifically, our real space resolution allows us to conclude that there is asharp distinction between the impurity being located at a crest or a troughsite at the zigzag edge. We also observe, as expected, that the spincorrelations are anisotropic due to an emerging Dzyaloshinskii-Moriyainteraction with the conduction electrons, and that the edges scatter from theimpurity and "snake" or circle around it. Our estimates for the Kondotemperature indicate that there is a very weak enhancement due to the presenceof spin-orbit coupling.

Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator