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Following the recent observation of the quantum spin Hall (QSH) effect inHgTe quantum wells, an important issue is to understand the effect ofimpurities on transport in the QSH regime. Using linear response andrenormalization group methods, we calculate the edge conductance of a QSHinsulator as a function of temperature in the presence of a magnetic impurity.At high temperatures, Kondo and/or two-particle scattering give rise to alogarithmic temperature dependence. At low temperatures, for weak Coulombinteractions in the edge liquid the conductance is restored to unitarity withunusual power-laws characteristic of a `local helical liquid', while for stronginteractions transport proceeds by weak tunneling through the impurity whereonly half an electron charge is transferred in each tunneling event.

Kondo effect in the helical edge liquid of the quantum spin Hall state