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In this work, a quantum dot couples to two helical edge states of a 2Dtopological insulator through weak tunnelings is studied. We show that if theelectron interactions on the edge states are repulsive, with Luttinger liquidparameter $ K < 1 $, the system flows to a stable two-channel fixed point atlow temperatures. This is in contrast to the case of a quantum dot couples totwo Luttinger liquid leads. In the latter case, a strong electron-electronrepulsion is needed, with $ K<1/2 $, to reach the two-channel fixed point. Thistwo-channel fixed point is described by a boundary Sine-Gordon Hamiltonian witha $K$ dependent boundary term. The impurity entropy at zero temperature isshown to be $ \ln\sqrt{2K} $. The impurity specific heat is $C \proptoT^{\frac{2}{K}-2}$ when $ 2/3 < K < 1 $, and $ C \propto T$ when $ K<2/3$. Wealso show that the linear conductance across the two helical edges hasnon-trivial temperature dependence as a result of the renormalization groupflow.

Quantum Dot in 2D Topological Insulator: The Two-channel Kondo Fixed Point