Two-spin entanglement induced by scattering of backscattering-free chiral electrons in a Chern insulator

Abstract

The existence of robust chiral edge states in a finite topologically nontrivial chern insulator is a consequence of the bulk-boundary correspondence. In this paper, we present a theoretical framework based on lattice Green's function to study the scattering of such chiral edge electrons by a single localized impurity. To this end, in the first step, we consider the standard topological Haldane model on a honeycomb lattice with strip geometry. We obtain analytical expressions for the wave functions and their corresponding energy dispersion of the low-energy chiral states localized at the edge of the ribbon. Then, we employ the $T$-matrix Lippmann-Schwinger approach to explicitly show the robustness of chiral edge states against the impurity scattering. This backscattering-free process has an interesting property that the transmitted wave function acquires an additional phase factor. Although this additional phase factor does not affect quantum transport through the chiral channel it can carry quantum information. As an example of such quantum information transport, we investigate the entanglement of two magnetic impurities in a chern insulator through the dissipation-less scattering of chiral electrons.