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.

References in corpus (21)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The space group classification of topological band insulators
• Helical Metal Inside a Topological Band Insulator
• Correlation effects in two-dimensional topological insulators
• Pseudomagnetic fields and ballistic transport in a suspended graphene sheet
• The Colored Hofstadter Butterfly for the Honeycomb Lattice
• Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum
• Band Collapse and the Quantum Hall Effect in Graphene
• Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice
• In-gap impurity states as the hallmark of the Quantum Spin Hall phase
• The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice
• Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution
• Impurity induced current in a Chern insulator

Cited by in corpus (10)

• 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