Impurity bound states as detectors of topological band structures revisited

Abstract

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126 (2015)] has argued, based on theoretical results for a particular class of models, that insulators with topologically trivial and non-trivial band structures in two space dimensions display a qualitatively different response to point-like impurities. Here we present a comprehensive investigation of the impurity response of a large set of models of non-interacting electrons on the honeycomb lattice, driven insulating by either broken inversion, broken time reversal, broken $C_3$, or broken translation symmetry. These cases include Hofstadter bands, strain-induced pseudo-Landau levels and higher-order topological insulators. Our results confirm that for hopping models respecting the lattice symmetries, the response to a single impurity can indeed distinguish between trivial and non-trivial band topology. However, for modulated or inhomogeneous host systems we find that trivial states of matter can display an impurity response akin to that of topologically non-trivial states, and thus the diagnostic fails.

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• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Magnon Interference Tunneling Spectroscopy as a Probe of 2D Magnetism
• Point-Gap Bound States in Non-Hermitian Systems
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Fractal defect states in the Hofstadter butterfly
• Local spin-flip transitions induced by magnetic quantum impurities in two-dimensional magnets
• Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism