Suppression of ballistic helical transport by isotropic dynamical magnetic impurities

Dynamical magnetic impurities (MI) are considered as a possible origin for suppression of the ballistic helical transport on edges of 2D topological insulators. The MIs provide a spin-flip backscattering of itinerant helical electrons. Such a backscattering reduces the ballistic conductance if the exchange interaction between the MI and the electrons is anisotropic and the Kondo screening is unimportant. It is well-known that the isotropic MIs do not suppress the helical transport in systems with axial spin symmetry of the electrons. We show that, if this symmetry is broken, the isotropic MI acquires an effective anisotropy and suppresses the helical conductance. The peculiar underlying mechanism is a successive backscattering of the electrons which propagate in the same direction and have different energies. The respective correction to the linear conductance is determined by the allowed phase space of the electrons and scales with temperature as T^4. Hence, it disappears at small temperatures. This qualitatively distinguishes effects governed by the MIs with the induced and bare anisotropy; the latter is temperature independent. If T is smaller than the applied bias, finite e V, the allowed phase space is provided by the bias and the differential conductance scales as (e V)^4.