Impurities in a Chern insulator

Vibhuti Bhushan Jha, Garima Rani, R. Ganesh

Published 2016-10-11Version 1

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 letter, 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 suffices to create bound states. We find analytic wavefunctions for the bound states and show that they carry a circulating current. In contrast, in the case of a trivial analogue -- 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. In all cases, our results compare well with numerical tight-binding results.