Helical edge transport in the presence of a magnetic impurity

Abstract

We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema. PACS:Introduction. -Two-dimensional topological insulators (2D TIs) are in the focus of recent interest due to existence of two helical edge states inside the band gap [1,2]. Because of spin-momentum locking caused by strong spin-orbit coupling, electrical current transfers helicity along the edge [3,4]. This "spin" current is a hallmark of the quantum spin Hall effect, and it has been detected experimentally in HgTe/CdTe quantum wells [5][6][7][8][9]. If only elastic scattering is allowed, and in the absence of time-reversal symmetry breaking, the helical state is a realization of the ideal transport channel with conductance of G 0 = e 2 /h. This prediction was questioned by the experiments in HgTe/CdTe [5,[10][11][12] and InAs/GaSb [13,14] quantum wells. Therefore, studies of mechanisms which can lead to the destruction of the ideal helical transport are important.A local perturbation breaking the time-reversal symmetry, e.g., a classical magnetic impurity, leads to backscattering of helical edge states and reduction of the edge conductance [15,16]. Electron-electron interactions along the edge can promote edge reconstruction and, consequently, spontaneous time-reversal symmetry breaking at the edge [17]. Furthermore, even in the absence of time-reversal symmetry breaking, electronelectron interactions may induce backscattering [18], resulting in the suppression of the helical edge conductance at finite temperatures (see [19] and references therein). A combination of electron-electron interactions and magnetic impurities can significantly modify the picture of ideal helical edge transport [20][21][22][23][24].In the absence of electron-electron interactions along the edge, the ideal transport along the helical edge may

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

“…We note that when considering the case of an impurity spin with spin larger than 1/2, the Hamiltonian may also include spin-anisotropy terms M α (S α ) 2 which are nontrivial. These terms may play an important role in driving backscattering current in such setups [45,47].…”

“…The question of the effect of magnetic impurities on the conductance along helical edges was the subject of theoretical attention as well, considering different forms of impurities, coupling, and electronic band structures [35][36][37][38][39][40][41][42][43][44][45][46][47]. At low temperatures and in the absence of strong electron-electron interactions, a generic magnetic impurity forms a Kondo singlet and is screened out, allowing the helical edge to reconstitute itself around it and, therefore, has no effect on the conductance.…”

“…They showed that this can be understood due to the fact that timereversal symmetry allows backscattering only accompanied with a spin-flip of the impurity, which can be further flipped back only with backscattering in the opposite direction, thus prohibiting a steady-state backscattered current. In order to circumvent this limitation while preserving time-reversal symmetry, one has to consider an anisotropic exchange coupling [38,[45][46][47] or describe coupling to a many-level interacting quantum dot [29,40,43].…”

Helical edge transport in the presence of a magnetic impurity: The role of local anisotropy

“…In what follows, we assume that the corresponding Kondo temperature is well below the relevant energy scales (related to the temperature, voltage, and local anisotropy), so that the renormalization of J ij can be neglected (see Appendix A). This is typically justified physically: for example, for Mn 2+ ion in a HgTe/CdTe quantum well J ij ∼ 10 −3 [47] and the corresponding Kondo temperature is extremely small (as compared to the energies accessible in transport experiments).…”

“…For V JT the solution for the steady state density matrix has a Gibbs form, with an effective temperature T eff that depends on the ratio V /T . [47] D. The overall behavior of the backscattering current for a half-integer spin…”