Conductance of a helical edge liquid coupled to a magnetic impurity

In a quantum spin Hall system, which can be realized in HeTe/(Hg,Cd)Te semiconductor quantum wells [1], helical edge states carry a current and the conductance takes the universal value of $2e^2/h$. This is because an impurity without internal degrees of freedom cannot backscatter an electron at the edge in the presence of time-reversal symmetry [2]. On the other hand, backscattering by a magnetic impurity is allowed. We study the effect of backscattering from a magnetic impurity on the conductance of a quantum spin Hall system [3], and obtain the correction $\delta G(\omega)$ to the electrical conductance as a function of frequency $\omega$. We find that the correction $\delta G(\omega)$ vanishes in the dc limit ($\omega \to 0$), when our model conserves the total spin $S_z$. Another interesting transport property is the thermal conductance, which is affected by the coupling to the magnetic impurity even at $\omega\to 0$. We find that the temperature dependence of the thermal conductance shows a non-monotonic behavior with a minimum occurring at the Kondo temperature. \\[4pt] [1] M. Konig {\it et al.}, Science 318, 766 (2007). \\[0pt] [2] C. Wu, B. A. Bernevig and S. C. Zhang, Phys. Rev. Lett. 96, 106401 (2006); C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006). \\[0pt] [3] J. Maciejko {\it et al.}, Phys. Rev. Lett. 102, 256803 (2009).