Two-dimensional topological insulators are have attracted much recent interest since they feature helical edge states inside their band gap [1,2]. In the absence of time-reversal symmetry breaking, spin-momentum locking prohibits elastic backscattering of these helical states, i.e., the helical edge is a realization of an ideal transport channel with conductance equal to e²/h. However, this theoretical prediction was not confirmed by experiments on HgTe/CdTe [3-6] and InAs/GaSb [7,8] quantum wells. The time-symmetric interaction of the helical states with a "quantum magnetic impurity'' (an impurity which has its own quantum dynamics) is a leading candidate for explaining these experiments. In spite of recent theoretical studies of this problem [9-14], several key questions has not been addressed in details.

 We study theoretically the modification of the ideal current-voltage characteristics of the helical edge in a two-dimensional topological insulator by weak scattering off a single magnetic impurity. As a physical realization of such a system we have in mind the (001) CdTe/HgTe/CdTe quantum well (QW) with a Mn impurity that possesses spin S=5/2. Contrary to previous works, we allow for a general structure of the matrix describing exchange interaction between the edge states and the magnetic impurity. For S=1/2 we find an analytical expression for the backscattering current at arbitrary voltage. For larger spin, S>1/2, we derive analytical expressions for the backscattering current at low and high voltages. We demonstrate that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema.

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      Kurilovich P.D. , Kurilovich V.D., Burmistrov I.S. , Goldstein M.                                                                               

JETP Letters 106 (9) (2017)