Kondo effect in a two-dimensional topological insulator: Exact results for adatom impurities

• Published in: The Journal of physics and chemistry of solids Vol. 128; no. C; pp. 202 - 206
• Main Authors: Allerdt, Andrew, Feiguin, A.E., Martins, G.B.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01-05-2019; Elsevier
• Subjects: Chemistry; Physics
• ISSN: 0022-3697; 1879-2553
• DOI: 10.1016/j.jpcs.2017.11.006

The Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] combined with density matrix renormalization group calculations is used to obtain exact real space properties of a model for a magnetic adatom impurity coupled to the edge of a zigzag stanene ribbon, which, given stanene's sizable spin-orbit interaction, has non-trivial topological properties. We consider an impurity coupled to a site from either sublattice A or B (where a zigzag edge can be pictured as ⋯/∖/∖⋯, or ⋯ABABA⋯, where a B-site, dubbed a crest site, is an outermost one, while an A-site is dubbed a trough site). Our real space resolution allows us to conclude that the two possible ground states are qualitatively very different: in both cases, the introduction of spin-orbit interaction greatly increases the range of the spin correlations between the impurity and the electron spins in the metallic edge-state; however, for the trough-site-coupled impurity the spin correlations show very strong anisotropy (〈Simp,zsz〉≠〈Simp,xsx〉, where Simp denotes the impurity spin and s denotes the spin of an electron in the lattice), while the spin correlations for the crest-coupled impurity are almost isotropic. These results suggest that for either type of site (crest or through) the problem can be mapped onto an Anderson impurity problem, with the adatom side-coupled to a one-dimensional channel. For the crest-coupled case this channel has practically trivial character, while for a trough site the spin-orbit interaction introduces a strong Dzyaloshinskii-Moriya interaction.