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

Abstract

We calculate exact zero-temperature real space properties of a substitutional magnetic impurity coupled to the edge of a zigzag silicene-like nanoribbon. Using a Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] and the density matrix renormalization group method, we obtain a realistic description of stanene and germanene that includes the bulk and the edges as boundary one-dimensional helical metallic states. Our results for substitutional impurities indicate that the development of a Kondo state and the structure of the spin correlations between the impurity and the electron spins in the metallic edge state depend considerably on the location of the impurity. More specifically, our real space resolution allows us to conclude that there is a sharp distinction between the impurity being located at a crest or a trough site at the zigzag edge. We also observe, as expected, that the spin correlations are anisotropic due to an emerging Dzyaloshinskii-Moriya interaction with the conduction electrons, and that the edges scatter from the impurity and "snake" or circle around it. Our estimates for the Kondo temperature indicate that there is a very weak enhancement due to the presence of spin-orbit coupling.

9 pages, 12 figures, to appear on PRB

References in corpus (20)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Energy Gaps in Graphene Nanoribbons
• Half-Metallic Graphene Nanoribbons
• Room temperature magnetic order on zigzag edges of narrow graphene nanoribbons
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Magnetic Correlations at Graphene Edges
• The development of ferromagnetism in the doped topological insulator Bi2-xMnxTe3
• RKKY in half-filled bipartite lattices: graphene as an example
• Diluted Graphene Antiferromagnet
• Charge transport through single molecules, quantum dots, and quantum wires
• Quantum impurity on the surface of a topological insulator
• Kondo effect on the surface of 3D topological insulators: Signatures in scanning tunneling spectroscopy
• Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice
• Kondo versus indirect exchange: the role of the lattice and the actual range of RKKY interactions in real materials
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• Kondo effect in graphene with Rashba spin-orbit coupling
• Kondo effect in a quantum wire with spin-orbit coupling
• Critical quasiparticles in single-impurity and lattice Kondo models

Cited by in corpus (6)

• An Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator
• Spin-1 two-impurity Kondo problem on a lattice
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Magnetic correlation between two local spins in a quantum spin Hall insulator
• Natural orbitals renormalization group approach to a spin-1/2 impurity interacting with two helical liquids
• Spin orbit interaction in nanotubes