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We study the conductance of a time-reversal symmetric helical electronic edgecoupled antiferromagnetically to a magnetic impurity, employing analytical andnumerical approaches. The impurity can reduce the perfect conductance $G_0$ ofa noninteracting helical edge by generating a backscattered current. Thebackscattered steady-state current tends to vanish below the Kondo temperature$T_K$ for time-reversal symmetric setups. We show that the central role inmaintaining the perfect conductance is played by a global $U(1)$ symmetry. Thissymmetry can be broken by an anisotropic exchange coupling of the helical modesto the local impurity. Such anisotropy, in general, dynamically vanishes duringthe renormalization group (RG) flow to the strong coupling limit atlow-temperatures. The role of the anisotropic exchange coupling is furtherstudied using the time-dependent Numerical Renormalization Group (TD-NRG)method, uniquely suitable for calculating out-of-equilibrium observables ofstrongly correlated setups. We investigate the role of finite bias voltage andtemperature in cutting the RG flow before the isotropic strong-coupling fixedpoint is reached, extract the relevant energy scales and the manner in whichthe crossover from the weakly interacting regime to the strong-couplingbackscattering-free screened regime is manifested. Most notably, we find thatat low temperatures the conductance of the backscattering current follows apower-law behavior $G\sim (T/T_K)^2$, which we understand as a strong nonlineareffect due to time-reversal symmetry breaking by the finite-bias.

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