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

TL;DR

This paper investigates the low-temperature behavior of a quantum dot coupled to two helical edge states in a 2D topological insulator, revealing a stable two-channel Kondo fixed point influenced by electron interactions.

Contribution

It demonstrates that weakly coupled quantum dots to helical edges can reach a two-channel Kondo fixed point under repulsive interactions, contrasting with previous models requiring stronger repulsion.

Findings

Stable two-channel fixed point for K<1 with weak tunneling

Impurity entropy at zero temperature is ln(√2K)

Temperature dependence of conductance shows non-trivial RG flow

Abstract

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