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

Abstract

We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the conductance of the backscattering current follows a power-law behavior $G\sim (T/T_K{)}^2$, which we understand as a strong nonlinear effect due to time-reversal symmetry breaking by the finite-bias.

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Cited by in corpus (8)

• Helical Liquids in Semiconductors
• Finite frequency backscattering current noise at a helical edge
• Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples
• Suppression of ballistic helical transport by isotropic dynamical magnetic impurities
• Two-channel Kondo problem in coupled interacting helical liquids
• RKKY to Kondo crossover in Helical Edge of a Topological Insulator
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Unidirectional magneto-transport of linearly dispersing topological edge states