Localization at the Edge of a 2D Topological Insulator by Kondo Impurities with Random Anisotropies

We consider chiral electrons moving along the one-dimensional helical edge of a two-dimensional topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.

Figure 1

Chiral electrons at the helical edge of a 2D TI interacting with localized spins. Solid arrows show the original impurity spins while the dashed arrows illustrate the tendency to ferromagnetic in-plane ordering of the impurity spins modified by the local rotations (8). In combination with this ordering, the random magnetic anisotropy leads to the backscattering of the edge electrons and thus to the destruction of the chirality due to the Anderson localization.