Impurity-bound states and Green's function zeros as local signatures of topology

2015/04/19 by Robert-Jan Slager, Louk Rademaker, Jan Zaanen +1 · 226 citations
Materials Science · Mathematics · Physics and Astronomy · #Bound state #Codimension #Combinatorics #Condensed matter physics #Eigenvalues and eigenvectors #Graphene research and applications #Impurity #Mathematical analysis #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.92.085126

published in Physical Review B 92(8) (American Physical Society) · 11 pages, 8 figures

arxiv created 2015/04/19 · openalex publication_date 2015/08/17 · arxiv updated 2015/08/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that the local in-gap Green's function of a band insulator G₀(\ensuremathε,k_\ensuremath∥,r_\ensuremath⊥=0), with r_\ensuremath⊥ the position perpendicular to a codimension-1 or codimension-2 impurity, reveals the topological nature of the phase. For a topological insulator, the eigenvalues of this Green's function attain zeros in the gap, whereas for a trivial insulator the eigenvalues remain nonzero. This topological classification is related to the existence of in-gap bound states along codimension-1 and codimension-2 impurities. Whereas codimension-1 impurities can be viewed as soft edges, the result for codimension-2 impurities is nontrivial and allows for a direct experimental measurement of the topological nature of two-dimensional insulators.

Citations

• Periodic table for topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors
• Topological Insulators with Inversion Symmetry
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological Crystalline Insulators
• Topological Insulators

Cited by

• Higher-Order Fabry-Pérot Interferometer from Topological Hinge States
• Impurity-induced current in a Chern insulator
• Quantum Dynamical Characterization and Simulation of Topological Phases With High-Order Band Inversion Surfaces
• Higher-order band topology
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Unified bulk-boundary correspondence for band insulators
• Phase-tunable second-order topological superconductor
• Second-Order Topological Superconductors with Mixed Pairing
• Impurity bound states as detectors of topological band structures revisited
• Type-II quadrupole topological insulators