2016/10/31 by Vibhuti Bhushan Jha, Garima Rani, R. Ganesh · 2 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Atomic and Subatomic Physics Research #Bound state #Condensed matter physics #Current (fluid) #Impurity #Infinitesimal #Invariant (physics) #Mathematics #Physics #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.95.115434
published as Phys. Rev. B 95, 115434 (2017)
arxiv created 2017/03/04 · openalex publication_date 2017/03/27 · arxiv updated 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Chern insulators arguably provide the simplest examples of topological phases. They are characterized by a topological invariant and can be identified by the presence of protected edge states. In this paper, we show that a local impurity in a Chern insulator induces a twofold response: bound states that carry a chiral current and a net current circulating around the impurity. This is a manifestation of broken time reversal symmetry and persists even for an infinitesimal impurity potential. To illustrate this, we consider a Coulomb impurity in the Haldane model. Working in the low-energy, long-wavelength limit, we show that an infinitesimal impurity strength suffices to create bound states. We find analytic wave functions for the bound states and show that they carry a circulating current. In contrast, in the case of a trivial analog---graphene with a gap induced by a sublattice potential---bound states occur but carry no current. In the many-body problem of the Haldane model at half-filling, we use a linear response approach to demonstrate a circulating current around the impurity. Impurity textures in insulators are generally expected to decay exponentially; in contrast, this current decays polynomially with distance from the impurity. Going beyond the Haldane model, we consider the case of coexisting trivial and nontrivial masses. We find that the impurity induces a local chiral current as long as time-reversal symmetry is broken. However, the decay of this local current bears a signature of the overall topology---the current decays polynomially in a nontrivial system and exponentially in a trivial system. In all cases, our analytic results agree well with numerical tight-binding simulations.